The Concentration of Measure PhenomenonAmerican Mathematical Soc., 2001 - 181 pages The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. This book offers the basic techniques and examples of the concentration of measure phenomenon. It presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications and product measures. |
Table des matières
Notes and Remarks | 21 |
Notes and Remarks | 44 |
Notes and Remarks | 65 |
Notes and Remarks | 89 |
Notes and Remarks | 115 |
15 | 119 |
21 | 127 |
Notes and Remarks | 132 |
Notes and Remarks | 149 |
32 | 155 |
Notes and Remarks | 170 |
| 171 | |
| 181 | |
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Expressions et termes fréquents
1-Lipschitz Anal applications Assume Banach spaces Bobkov Borel sets canonical Gaussian measure Chapter concentration function concentration inequalities concentration of measure concentration properties Corollary defined definition denote deviation inequalities differential inequality dimension free dimensional empirical processes entropy Euclidean example exponential distribution finite first follows Funct function F Gaussian measures geometric Hamming metric independent random variables integrability isoperimetric inequality Laplace Lebesgue measure Lemma Let F Lévy family Lipschitz functions logarithmic Sobolev inequalities Markov chain martingale measurable functions measure concentration measure phenomenon measure µ metric space non-negative norm normal concentration Notes in Math numerical constant particular Poincaré inequality probability measure probability space product measure product space proof of Theorem Proposition quadratic transportation cost respect Riemannian manifold satisfies Section 4.2 semigroup sphere Springer subset sums of independent supremum supteT symmetric Tal7 Talagrand Theorem 4.6 transportation cost inequality V. D. Milman