Concentration of measure and logarithmic Sobolev inequalities









Logarithmic Sobolev Inequalities

logarithmic Sobolev inequalities what they are some history analytic
Logsobwpause


Logarithmic Sobolev Inequalities

LOGARITHMIC SOBOLEV INEQUALITIES. By LEONARD GRoss.*. 1. Introduction. Classical Sobolev inequalities state typically


Lectures on Logarithmic Sobolev Inequalities

Jan 1 2012 Section 4.1 Properties of logarithmic Sobolev inequality ... ing to learn how to prove log-Sobolev inequality in infinite-dimensional ...
SPS


1 CONCENTRATION OF MEASURE AND LOGARITHMIC

2.2 Examples of logarithmic Sobolev inequalities p. 26. 2.3 The Herbst argument p. 29. 2.4 Entropy-energy inequalities and non-Gaussian tails.
Berlin





Mass transport and variants of the logarithmic Sobolev inequality

Sep 25 2007 Abstract. We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities.


Modified Log-Sobolev Inequalities Mixing and Hypercontractivity

These inequalities turn out to be weaker than the stan- dard log-Sobolev inequality but stronger than the Poincare'. (spectral gap) inequality.
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Concentration of measure and logarithmic Sobolev inequalities

4.3 Poincare inequalities and modified logarithmic Sobolev inequalities 5.1 Logarithmic Sobolev inequality for Bernoulli and Poisson measures.
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Logarithmic Sobolev inequalities for unbounded spin systems revisited

or logarithmic Sobolev inequality and to control the dependence of the Logarithmic Sobolev inequalities for compact spin systems have been studied.
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Logarithmic Sobolev Inequalities Essentials: Probabilistic Side

Logarithmic Sobolev Inequalities Essentials: Probabilistic Side. High dimensional probability. Rough lecture notes. Djalil Chafaï & Joseph Lehec.
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Analytic and Geometric Logarithmic Sobolev Inequalities

One basic form of the logarithmic Sobolev inequality is the one for the standard. Gaussian probability measure dµ(x) = (2π)−n/2 e−
jedp.


213442 Concentration of measure and logarithmic Sobolev inequalities SÉMINAIRE DE PROBABILITÉS(STRASBOURG)MICHELLEDOUX

Concentrationofmeasureandlogarithmic

Sobolevinequalities

Séminaire de probabilités (Strasbourg), tome 33 (1999), p. 120-216 © Springer-Verlag, Berlin Heidelberg New York, 1999, tous droits réservés. L"accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l"accord avec les conditions générales d"utili- sation (http://www.numdam.org/conditions). Toute utilisation commerciale ou im- pression systématique est constitutive d"une infraction pénale. Toute copie ou im-

pression de ce fichier doit contenir la présente mention de copyright.Article numérisé dans le cadre du programme

Numérisation de documents anciens mathématiques http://www.numdam.org/

CONCENTRATION OF MEASURE

AND LOGARITHMIC SOBOLEV

INEQUALITIES

MICHEL LEDOUX

TABLE OF CONTENTS

INTRODUCTION 123

1. ISOPERIMETRIC AND CONCENTRATION

INEQUALITIES 126

1.1 Introduction

126
1.2

Isoperimetric inequalities

for Gaussian and Boltzmann measures 127

1.3 Some

general facts about concentration 134

2. SPECTRAL GAP AND LOGARITHMIC SOBOLEV

INEQUALITIES

139

2.1 Abstract functional

inequalities 139
2.2

Examples

of logarithmic

Sobolev

inequalities 145

2.3 Herbst's

argument 148
2.4

Entropy-energy inequalities

and non-Gaussian tails 154

2.5 Poincare

inequalities and concentration 159

3. DEVIATION

INEQUALITIES

FOR PRODUCT MEASURES 161

3.1 Concentration with

respect to the

Hamming

metric 161

3.2 Deviation

inequalities for convex functions 163

3.3 Information

inequalities and concentration 166
3.4

Applications

to bounds on empirical processes 171

4. MODIFIED LOGARITHMIC SOBOLEV

INEQUALITIES

FOR

LOCAL GRADIENTS 173

4.1 The

exponential measure 173

4.2 Modified

logarithmic

Sobolev

inequalities 178

4.3 Poincare

inequalities and modified logarithmic

Sobolev

SÉMINAIRE DE PROBABILITÉS(STRASBOURG)MICHELLEDOUX

Concentrationofmeasureandlogarithmic

Sobolevinequalities

Séminaire de probabilités (Strasbourg), tome 33 (1999), p. 120-216 © Springer-Verlag, Berlin Heidelberg New York, 1999, tous droits réservés. L"accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l"accord avec les conditions générales d"utili- sation (http://www.numdam.org/conditions). Toute utilisation commerciale ou im- pression systématique est constitutive d"une infraction pénale. Toute copie ou im-

pression de ce fichier doit contenir la présente mention de copyright.Article numérisé dans le cadre du programme

Numérisation de documents anciens mathématiques http://www.numdam.org/

CONCENTRATION OF MEASURE

AND LOGARITHMIC SOBOLEV

INEQUALITIES

MICHEL LEDOUX

TABLE OF CONTENTS

INTRODUCTION 123

1. ISOPERIMETRIC AND CONCENTRATION

INEQUALITIES 126

1.1 Introduction

126
1.2

Isoperimetric inequalities

for Gaussian and Boltzmann measures 127

1.3 Some

general facts about concentration 134

2. SPECTRAL GAP AND LOGARITHMIC SOBOLEV

INEQUALITIES

139

2.1 Abstract functional

inequalities 139
2.2

Examples

of logarithmic

Sobolev

inequalities 145

2.3 Herbst's

argument 148
2.4

Entropy-energy inequalities

and non-Gaussian tails 154

2.5 Poincare

inequalities and concentration 159

3. DEVIATION

INEQUALITIES

FOR PRODUCT MEASURES 161

3.1 Concentration with

respect to the

Hamming

metric 161

3.2 Deviation

inequalities for convex functions 163

3.3 Information

inequalities and concentration 166
3.4

Applications

to bounds on empirical processes 171

4. MODIFIED LOGARITHMIC SOBOLEV

INEQUALITIES

FOR

LOCAL GRADIENTS 173

4.1 The

exponential measure 173

4.2 Modified

logarithmic

Sobolev

inequalities 178

4.3 Poincare

inequalities and modified logarithmic

Sobolev


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