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Stability of precise Laplace's method under approximations;Applications

Published online by Cambridge University Press:  15 August 2002

A. Guionnet
A. Guionnet*
Affiliation:
URA 743 du CNRS, bâtiment 425, Université de Paris Sud, 91405 Orsay, France.
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Abstract

We study the fluctuations around non degenerate attractors of the empirical measure under mean field Gibbs measures. We prove that a mild change of the densities of these measures does not affect the central limit theorems. We apply this result to generalize the assumptions of [3] and [12] on the densities of the Gibbs measures to get precise Laplace estimates.

Keywords

Large deviationcentral limit theoremU-statistics.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 3 , 1999 , pp. 67 - 88
Copyright
© EDP Sciences, SMAI, 1999

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