Displaying similar documents to “Integral criteria for transportation-cost inequalities.”

Conditional principles for random weighted measures

Nathael Gozlan (2005)

ESAIM: Probability and Statistics

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In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form L n = 1 n ∑ i = 1 n Z i δ x i n , ( Z i ) i being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.

Deviation bounds for additive functionals of Markov processes

Patrick Cattiaux, Arnaud Guillin (2008)

ESAIM: Probability and Statistics

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In this paper we derive non asymptotic deviation bounds for ν ( | 1 t ∫ 0 t V ( X s ) d s - ∫ V d μ | ≥ R ) where X is a μ stationary and ergodic Markov process and V is some μ integrable function. These bounds are obtained under various moments assumptions for V , and various regularity assumptions for μ . Regularity means here that μ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc.).

Functional inequalities and uniqueness of the Gibbs measure — from log-Sobolev to Poincaré

Pierre-André Zitt (2008)

ESAIM: Probability and Statistics

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In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow Royer's approach (Royer, 1999) and obtain uniqueness by showing convergence properties of a Glauber-Langevin dynamics. The result was known when the measures on the box [- (with free boundary conditions) satisfied the same logarithmic Sobolev inequality. We generalize this in two directions: either the constants...

Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

Radosław Adamczak, Michał Strzelecki (2015)

Studia Mathematica

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We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev...