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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60E15 Inequalities (Chebyshev, Kolmogorov, etc.)
- 60F05 Central limit and other weak theorems
- 94A17 Measures of information, entropy
- 60G42 Martingales with discrete parameter

**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*