Speaker
Meliot, Université Paris-Saclay
Abstract
Consider a Brownian motion \(B_t on U(n)\) started from \(B_0 = I_n\), and the characteristic polynomial \(P_t(z)\) of \(B_t\). The main coefficients of \(P_t(z)\) all converge towards their limiting laws around the same time \(t = 4\ log n\). In this talk, we shall explain this phenomenon, and then expand the result to certain diffusions on compact matrix groups which are not elliptic, but hypoelliptic. These diffusions are related to compact symmetric spaces and to specific sub-Riemannian geometries of the compact Lie groups.