Large Deviations for Symmetrised Empirical Measures

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^{n}_{i},X^{n}_{sigma_{n}(i)})}) 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.