Large deviations for symmetrised empirical measures

Abstract

In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures $\frac{1}{n}{\sum }_{i=1}^n{\delta }_{(X_i^n,X_{{\sigma }_n(i)}^n)}$ where ${\sigma }_n$ is a random permutation and $((X_i^n{)}_{1\le i\le n}{)}_{n\ge 1}$ 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.