Lectures on 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 ...
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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−
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213530 Lectures on Logarithmic Sobolev Inequalities SÉMINAIRE DE PROBABILITÉS(STRASBOURG)A.GUIONNET

B.ZEGARLINSKI

LecturesonLogarithmicSobolevInequalities

Séminaire de probabilités (Strasbourg), tome 36 (2002), p. 1-134 © Springer-Verlag, Berlin Heidelberg New York, 2002, 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/

Lectures on

Logarithmic

Sobolev

Inequalities

by

A. Guionnet 1 and B.

Zegarlinski 2

Contents

Introduction.

Chapter

1. Markov

semi-groups

Section 1.1 Markov

semi-groups and Generators

Section 1.2 Invariant measures of a

semi-group

Section 1.3 Markov

processes

Chapter

2.

Spectral gap inequality

and L2 ergodicity

Chapter

3. Classical Sobolev

inequalities and ultracontractivity

Chapter

4.

Logarithmic

Sobolev

inequalities and hypercontractivity

Section 4.1

Properties

of logarithmic

Sobolev

inequality

Section 4.2

Logarithmic

Sobolev and

Spectral Gap inequalities

Section 4.3

Bakry-Emery

Criterion

Chapter

5.

Logarithmic

Sobolev

inequalities for spin systems on a lattice

Section 5.1 Notation and

definitions, statistical mechanics

Section 5.2

Strategy

to demonstrate the logarithmic

Sobolev

inequality

Section 5.3

Logarithmic

Sobolev

inequality in dimension 1; an example

Section 5.4

Logarithmic

Sobolev

inequalities in dimension > 2

Chapter

6.

Logarithmic

Sobolev

inequalities and cellular automata

Chapter

7.

Logarithmic

Sobolev

inequalities for spin systems with long range interaction.

Martingale expansion

Chapter

8. Markov

semi group in infinite SÉMINAIRE DE PROBABILITÉS(STRASBOURG)A.GUIONNET

B.ZEGARLINSKI

LecturesonLogarithmicSobolevInequalities

Séminaire de probabilités (Strasbourg), tome 36 (2002), p. 1-134 © Springer-Verlag, Berlin Heidelberg New York, 2002, 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/

Lectures on

Logarithmic

Sobolev

Inequalities

by

A. Guionnet 1 and B.

Zegarlinski 2

Contents

Introduction.

Chapter

1. Markov

semi-groups

Section 1.1 Markov

semi-groups and Generators

Section 1.2 Invariant measures of a

semi-group

Section 1.3 Markov

processes

Chapter

2.

Spectral gap inequality

and L2 ergodicity

Chapter

3. Classical Sobolev

inequalities and ultracontractivity

Chapter

4.

Logarithmic

Sobolev

inequalities and hypercontractivity

Section 4.1

Properties

of logarithmic

Sobolev

inequality

Section 4.2

Logarithmic

Sobolev and

Spectral Gap inequalities

Section 4.3

Bakry-Emery

Criterion

Chapter

5.

Logarithmic

Sobolev

inequalities for spin systems on a lattice

Section 5.1 Notation and

definitions, statistical mechanics

Section 5.2

Strategy

to demonstrate the logarithmic

Sobolev

inequality

Section 5.3

Logarithmic

Sobolev

inequality in dimension 1; an example

Section 5.4

Logarithmic

Sobolev

inequalities in dimension > 2

Chapter

6.

Logarithmic

Sobolev

inequalities and cellular automata

Chapter

7.

Logarithmic

Sobolev

inequalities for spin systems with long range interaction.

Martingale expansion

Chapter

8. Markov

semi group in infinite
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