Vortrag von P. Graczyk (Université d'Angers, Frankreich) zum Thema "Integral kernels for complex symmetric spaces and radial Dunkl processes"
We consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, Newton, Poisson kernels and spherical functions. We derive two-sided bounds for the Newton and Poisson kernels of the invariant Dunkl process in the direct product case. We introduce and exploit a simple new method of construction of these invariant kernels by alternating sums. We then use the alternating sum representation of these kernels to obtain their asymptotic behavior. We apply our results to the Dyson Brownian Motion in a Weyl chamber.
This is a joint work with T. Luks (Paderborn) and P. Sawyer (Sudbury).