Stability of precise Laplace's method under approximations; Applications

A. Guionnet

ESAIM: Probability and Statistics (2010)

  • Volume: 3, page 67-88
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Guionnet, A.. "Stability of precise Laplace's method under approximations; Applications." ESAIM: Probability and Statistics 3 (2010): 67-88. <http://eudml.org/doc/197763>.

@article{Guionnet2010,
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. },
author = {Guionnet, A.},
journal = {ESAIM: Probability and Statistics},
keywords = {Large deviation; central limit theorem; U-statistics.; central limit theorems; Gibbs measures; Laplace estimates},
language = {eng},
month = {3},
pages = {67-88},
publisher = {EDP Sciences},
title = {Stability of precise Laplace's method under approximations; Applications},
url = {http://eudml.org/doc/197763},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Guionnet, A.
TI - Stability of precise Laplace's method under approximations; Applications
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 67
EP - 88
AB - 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.
LA - eng
KW - Large deviation; central limit theorem; U-statistics.; central limit theorems; Gibbs measures; Laplace estimates
UR - http://eudml.org/doc/197763
ER -

References

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  14. K.R. Parthasarathy, Probability measures on Metric Spaces. Academic Press Inc., New York (1968).  Zbl0153.19101
  15. V.H. De La Pena, Decoupling and Khintchine's inequalities for U-statistics. Ann. Probab. 20 (1992) 1877-1892.  Zbl0761.60014
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