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Conditional principles for random weighted measures

Published online by Cambridge University Press:  15 November 2005

Nathael Gozlan
Nathael Gozlan*
Affiliation:
Université Paris 10-Nanterre, équipe MODAL'X, UFR SEGMI, 200 avenue de la République, 92001 Nanterre, Cedex, France; nathael.gozlan@u-paris10.fr
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Abstract

In this paper, we prove a conditional principle of Gibbs type forrandom weighted measures of the form ${L_n=\frac{1}{n}\sum_{i=1}^nZ_i\delta_{x_i^n}}$ , ((Zi)i being asequence of i.i.d. real random variables. Our work extends thepreceding results of Gamboa and Gassiat (1997), in allowing to consider thinconstraints. Transportation-like ideas are used in the proof.

Keywords

Large deviationstransportation cost inequalitiesconditional laws of large numbersminimum entropy methods.

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 9 , February 2005 , pp. 283 - 306
Copyright
© EDP Sciences, SMAI, 2005

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