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.
STOC BT
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.
SPS
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.
SPS
Logarithmic Sobolev Inequalities Essentials: Probabilistic Side
Logarithmic Sobolev Inequalities Essentials: Probabilistic Side. High dimensional probability. Rough lecture notes. Djalil Chafaï & Joseph Lehec.
chafai lehec m lsie lecture notes
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.
SÉMINAIRE DE PROBABILITÉS(STRASBOURG)MICHELLEDOUX LogarithmicSobolevinequalitiesforunbounded
spinsystemsrevisited Séminaire de probabilités (Strasbourg), tome 35 (2001), p. 167-194pression 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/LOGARITHMIC
SOBOLEV
INEQUALITIES
FOR UNBOUNDED SPIN SYSTEMS REVISITED
M. LEDOUX
University of Toulouse,
France
Abstract.
We analyze recent proofs of decay of correlations and logarithmicSobolev
inequalities for unbounded spin systems in the perturbative regime developed by B.Zegarlinski,
N.Yoshida,
B.Helfler,
Th. Bodineau. We
investigate to this task a simple analytic model.Proofs
are short and self-contained. Let be a probability measure on R satisfying, for some constant C > 0 and for every smooth enough function f on R, either the Poincaré (or spectral gap) inequality C where is the variance of f with respect to (see below), or the logarithmicSobolev
inequality C where is the entropy of f 2 with respect to (see below).It is well-known
that the product measure of on l~n then satisfies the preceding inequalities (with the Euclidean length of the gradient of the function f on JRn) with the same constant C, in particular independent of the dimension n.Let now H be a smooth function on l~n such
that J e-H df.-ln oo. Define Q the probability measure on with density1 Ze-H
with respect to where Z is the normalization factor. It is a natural question to ask under which conditions on H, the probability measure Q will satisfy a Poincaré or SÉMINAIRE DE PROBABILITÉS(STRASBOURG)MICHELLEDOUXLogarithmicSobolevinequalitiesforunbounded
spinsystemsrevisited Séminaire de probabilités (Strasbourg), tome 35 (2001), p. 167-194pression 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/LOGARITHMIC
SOBOLEV
INEQUALITIES
FOR UNBOUNDED SPIN SYSTEMS REVISITED
M. LEDOUX
University of Toulouse,
France
Abstract.
We analyze recent proofs of decay of correlations and logarithmicSobolev
inequalities for unbounded spin systems in the perturbative regime developed by B.Zegarlinski,
N.Yoshida,
B.Helfler,
Th. Bodineau. We
investigate to this task a simple analytic model.Proofs
are short and self-contained. Let be a probability measure on R satisfying, for some constant C > 0 and for every smooth enough function f on R, either the Poincaré (or spectral gap) inequality C where is the variance of f with respect to (see below), or the logarithmicSobolev
inequality C where is the entropy of f 2 with respect to (see below).It is well-known
that the product measure of on l~n then satisfies the preceding inequalities (with the Euclidean length of the gradient of the function f on JRn) with the same constant C, in particular independent of the dimension n.Let now H be a smooth function on l~n such
that J e-H df.-ln oo. Define Q the probability measure on with density1 Ze-H
with respect to where Z is the normalization factor. It is a natural question to ask under which conditions on H, the probability measure Q will satisfy a Poincaré or- log-sobolev inequality for the continuum sine-gordon model
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