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Journals and Conferences
We study coercive inequalities in Orlicz spaces associated to the probability measures on finite and infinite dimensional spaces which tails decay slower than the Gaussian ones. We provide necessary and sufficient criteria for such inequalities to hold and discuss relations between various classes of inequalities. Mathematics Subject Classification: 60E15,… (More)
This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as weak Poincaré and weak Cheeger, weighted Poincaré and weighted Cheeger inequalities and their dual forms. Proofs are short and we cover very large situations.… (More)
We give a characterization of transport-entropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley–Stroock perturbation lemma). 1. Introduction. In their celebrated paper , Otto and Villani proved that, in a smooth Riemannian setting, the log-Sobolev inequality implies the… (More)
We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and Götze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo.
We prove that for symmetric Markov processes of diffusion type admitting a " carré du champ " , the Poincaré inequality is equivalent to the exponential convergence of the associated semi-group in one (resp. all) L p (µ) spaces for 1 < p < +∞. We also give the optimal rate of convergence. Part of these results extends to the stationary, not necessarily… (More)
We analyze the density and size dependence of the relaxation time for kinetically constrained spin models (KCSM) intensively studied in the physical literature as simple models sharing some of the features of a glass transition. KCSM are interacting particle systems on Z with Glauber-like dynamics, reversible w.r.t. a simple product i.i.d Bernoulli(p)… (More)
We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails. Spins are unbounded. The interactions are bounded and finite range. The self potential enters into two classes of measures, κ-concave probability measure and sub-exponential laws, for which it is known that no exponential decay can occur. We prove, using coercive… (More)
We consider the Fredrickson and Andersen one spin facilitated model (FA1f) on an infinite connected graph with polynomial growth. Each site with rate one refreshes its occupation variable to a filled or to an empty state with probability p ∈ [0, 1] or q = 1 − p respectively, provided that at least one of its nearest neighbours is empty. We study the… (More)
We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are approximate solutions of the isoperimetric problem.