Large deviations of empirical measures under symmetric interaction

2002/03/31 by Wlodek Bryc
Mathematics · #math.PR

paper · pdf

published as Journ. Theoret. Probab. 16 (2003) pp. 935-955 · LaTeX, 15 pages

arxiv created 2003/12/02 · arxiv updated 2009/11/30

Abstract

In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product measures and hence is non-convex. As a corollary, we derive a large deviations principle for (univariate) average empirical measures with the rate function that superficially resembles the rate function of random matrices, but may be concave.

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