Large deviations for symmetrised empirical measures.

In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures TeX where σ n is a random permutation and ((X i n )1≤i≤n ) n≥1 is a triangular array of random variables with suitable properties. As an application we show how this result allows to improve the Large Deviation Principles for symmetrised initial-terminal conditions bridge processes recently established by Adams, Dorlas and König.ou