Some Martingales Associated With Multivariate Bessel Processes.

We study Bessel processes on Weyl chambers of types A and B on R N . Using elementary symmetric functions, we present several space-timeharmonic functions and thus martingales for these processes (X t) t ≥ 0 which are independent from one parameter of these processes. As a consequence, p t (y) : = E (∏ i = 1 N (y - X t i)) can be expressed via classical orthogonal polynomials. Such formulas on characteristic polynomials admit interpretations in random matrix theory where they are partially known by Diaconis, Forrester, and Gamburd. [ABSTRACT FROM AUTHOR]