virtuell

Consider Bessel, Jacobi, and Dunkl processes on RN which depend on several positive coupling constants k . These processes describe interacting particle systems of Calogero-Moser-Sutherland type with N particles. For some cases, these processes are related with β -Hermite, -Laguerre, and -Jacobi ensembles. Moreover, for the frozen case k=∞ , the processes degenerate to deterministic or pure jump processes. We show how the generators for these processes lead to analogues of Wigner's semicircle and Marchenko-Pastur limit laws for N→∞ for the empirical distributions of the particles with arbitrary initial empirical distributions by using free convolutions. In the frozen cases, our approach leads to a new proof of well known limit laws for the empirical measures of the zeroes of Hermite, Laguerre, and Jacobi polynomials. The talk is based on joint work with J. Woerner and M. Auer.

Hörer sollten sich bitte im Moodle-Raum https://moodle.tu-dortmund.de/enrol/index.php?id=23191 des Seminars anmelden. An alle Angemeldeten werden die Zugangsdaten zum meeting geschickt Weitere Vorträge in der Reihe sind unter http://www.mathematik.tu-dortmund.de/lsix/lehre/WiSe2021/GRK-Seminar/index.php einsehbar.

Michael Voit

TU Dortmund