Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Free energy estimates and deviation inequalities


Code(s) de Classification MSC:

Résumé: Using ``free energy estimates'', we give non asymptotic bounds for the log Laplace transform of a function of $N$ random variables. We assume either that these random variables are independent or that they form a Markov chain. We assume also that the partial finite differences of order one and two of the function are bounded, or more generally that they have exponential moments. The estimates of the log Laplace transform we get are sharp enough to induce a central limit theorem when $N$ goes to infinity and to prove non asymptotic ``almost Gaussian'' deviation bounds.

Mots Clés: Concentration of product measures ; Deviation inequalities ; Markov chains ; Maximal coupling ; Central limit theorem

Date: 1999-12-02

Prépublication numéro: PMA-545

Revised version