Piotr Graczyk (Universit茅 d'Angers)
Title: Estimates of kernels associated with the Dyson and Dunkl processes.
Abstract: Dyson and Dunkl processes are听important stochastic processes modelizing uncolliding particle systems.听 Uncolliding Brownian particles were听introduced听by Dyson in 1962 and听later called Dyson Brownian Motion.
It is a special case of听radial Dunkl processes, called also听multivariate Bessel processes. Dunkl operators were discovered by Dunkl in late 1980鈥檚 as a crucial tool to study Calogero-Moses-Sutherland mechanical particle systems.听 Dunkl processes听 were introduced听by Roesler and Voit in 1998 and studied also by Gallardo and Yor.听听听
In this talk I will present recent estimates of听 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.
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