ESAIM: Probability and Statistics

Table of Contents - November 2005 - Volume 9  

Research Article

Conditional principles for random weighted measures

Gozlan, Nathael

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

Abstract

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

(Received October 25 2004)

(Revised April 7 2005)

(Online publication November 15 2005)

Key Words:

  • Large deviations;
  • transportation cost inequalities;
  • conditional laws of large numbers;
  • minimum entropy methods.

Mathematics Subject Classification:

  • 60E15;
  • 60F10
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