*Journées de Probabilités 2007*

**Marguerite Zani **

*Large deviations for statistics of Jacobi processes *

(In collaboration with N. Demni)

We derive large deviations for statistics of Jacobi processes. To proceed, we write in a more simple way the Jacobi semi-group density. Being given by a bilinear sum involving Jacobi polynomials, it differs from Hermite and Laguerre cases by the quadratic form of its eigenvalues. Our attempt relies on subordinating the process using a suitable random time-change. We can recover the desired expression by inverting some Laplace tranforms. Then we conclude with a large deviations principle in a non steep-case.