Piotr Graczyk (Université d'Angers)

Title: Estimates of kernels associated with the Dyson and Dunkl processes.

Abstract: Dyson and Dunkl processes are important stochastic processes modelizing uncolliding particle systems.  Uncolliding Brownian particles were introduced by Dyson in 1962 and later called Dyson Brownian Motion.

It is a special case of radial Dunkl processes, called also multivariate Bessel processes. Dunkl operators were discovered by Dunkl in late 1980’s as a crucial tool to study Calogero-Moses-Sutherland mechanical particle systems.  Dunkl processes  were introduced by Roesler and Voit in 1998 and studied also by Gallardo and Yor.   

In this talk I will present recent estimates of  Poisson, Newton and Heat kernels for radial Dunkl processes, obtained in collaboration with Patrice Sawyer (Laurentian University). Our methods are based on harmonic and potential analysis related to root systems.