concentration of measure and isoperimetric inequalities in

133
CONCENTRATION OF MEASURE AND ISOPERIMETRIC INEQUALITIES IN PRODUCT b y MICHEL TALAGRAND SPACES ABSTRACT. The concent ration of measure phenome non in product spaces roughl y states that, if a set A in a pr oduct .QN of probability spaces has measure at least one half, " most " of the points of ON are " close " to A. We proceed to a systematic exploration of this phenomenon. The meaning of the word " most " is made rigorous by isoperimetric- type inequalit ies that bound the measure of the exceptional sets. The meaning of the work" close " is defined in three ma in ways, each of them giving rise to related, but different inequalities. The inequalities are all proved thr ough a common scheme of proof. Remarkably, this simple approach not only yields qualitatively optimal results, but, in many cases, captures near optimal numerical constants. A large number of applications are given, in particular to Percolation, Geometric Probability, Probability in Banach Spaces, to demonstrate in concrete situations the extremely wide range of application of the abstract tools. TABLE OF CONTENTS I. INEQUALITIES ............................................................................. 74 1. Introduaion .............................................................................. 74 2. Control by one point ....................................................................... 81 2.1. Basic principle ..................................................................... 81 2.2. Sharpening ......................................................................... 85 2.3. Two point space ................................................................... 87 2.4. Penalties, I ........................................................................ 91 2.5. Penalties, II ....................................................................... 94 2.6. Penalties, III ....................................................................... 96 2.7. Penalties, IV ....................................................................... 103 3. Control by q points ........................................................................ 112 3.1. Baste result ........................................................................ 113 3.2. Sharpening ......................................................................... 114 3.3. Penalties ........................................................................... 11 5 3.4. Interpolation ....................................................................... 120 AMS Classification numbers: Primary 60E15, 28A35, 60G99; Secondary 60G15, 68C15. 10

Upload: api-24646577

Post on 30-May-2018

216 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 1/133

Page 2: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 2/133

Page 3: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 3/133

Page 4: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 4/133

Page 5: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 5/133

Page 6: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 6/133

Page 7: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 7/133

Page 8: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 8/133

Page 9: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 9/133

Page 10: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 10/133

Page 11: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 11/133

Page 12: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 12/133

Page 13: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 13/133

Page 14: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 14/133

Page 15: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 15/133

Page 16: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 16/133

Page 17: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 17/133

Page 18: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 18/133

Page 19: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 19/133

Page 20: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 20/133

Page 21: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 21/133

Page 22: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 22/133

Page 23: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 23/133

Page 24: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 24/133

Page 25: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 25/133

Page 26: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 26/133

Page 27: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 27/133

Page 28: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 28/133

Page 29: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 29/133

Page 30: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 30/133

Page 31: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 31/133

Page 32: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 32/133

Page 33: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 33/133

Page 34: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 34/133

Page 35: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 35/133

Page 36: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 36/133

Page 37: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 37/133

Page 38: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 38/133

Page 39: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 39/133

Page 40: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 40/133

Page 41: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 41/133

Page 42: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 42/133

Page 43: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 43/133

Page 44: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 44/133

Page 45: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 45/133

Page 46: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 46/133

Page 47: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 47/133

Page 48: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 48/133

Page 49: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 49/133

Page 50: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 50/133

Page 51: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 51/133

Page 52: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 52/133

Page 53: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 53/133

Page 54: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 54/133

Page 55: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 55/133

Page 56: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 56/133

Page 57: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 57/133

Page 58: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 58/133

Page 59: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 59/133

Page 60: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 60/133

Page 61: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 61/133

Page 62: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 62/133

Page 63: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 63/133

Page 64: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 64/133

Page 65: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 65/133

Page 66: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 66/133

Page 67: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 67/133

Page 68: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 68/133

Page 69: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 69/133

Page 70: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 70/133

Page 71: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 71/133

Page 72: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 72/133

Page 73: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 73/133

Page 74: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 74/133

Page 75: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 75/133

Page 76: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 76/133

Page 77: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 77/133

Page 78: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 78/133

Page 79: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 79/133

Page 80: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 80/133

Page 81: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 81/133

Page 82: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 82/133

Page 83: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 83/133

Page 84: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 84/133

Page 85: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 85/133

Page 86: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 86/133

Page 87: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 87/133

Page 88: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 88/133

Page 89: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 89/133

Page 90: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 90/133

Page 91: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 91/133

Page 92: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 92/133

Page 93: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 93/133

Page 94: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 94/133

Page 95: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 95/133

Page 96: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 96/133

Page 97: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 97/133

Page 98: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 98/133

Page 99: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 99/133

Page 100: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 100/133

Page 101: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 101/133

Page 102: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 102/133

Page 103: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 103/133

Page 104: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 104/133

Page 105: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 105/133

Page 106: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 106/133

Page 107: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 107/133

Page 108: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 108/133

Page 109: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 109/133

Page 110: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 110/133

Page 111: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 111/133

Page 112: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 112/133

Page 113: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 113/133

Page 114: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 114/133

Page 115: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 115/133

Page 116: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 116/133

Page 117: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 117/133

Page 118: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 118/133

Page 119: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 119/133

Page 120: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 120/133

Page 121: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 121/133

Page 122: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 122/133

Page 123: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 123/133

Page 124: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 124/133

Page 125: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 125/133

Page 126: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 126/133

Page 127: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 127/133

Page 128: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 128/133

Page 129: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 129/133

Page 130: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 130/133

Page 131: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 131/133

Page 132: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 132/133

Page 133: Concentration of Measure and Isoperimetric Inequalities In

8/9/2019 Concentration of Measure and Isoperimetric Inequalities In

http://slidepdf.com/reader/full/concentration-of-measure-and-isoperimetric-inequalities-in 133/133