Brownian motion on the unitary group and random walk on the symmetric group
主 题: Brownian motion on the unitary group and random walk on the symmetric group
报告人: Prof. Thierry Levy (CNRS, ENS Paris)
时 间: 2008-10-21 上午 10:00 - 11:00
地 点: 理科一号楼 1303
We will discuss the Brownian motion on the unitary group U(N) and its
limit when N tends to infinity. This limit has been investigated by P.
Biane and F. Xu aroud 1996 and more recently by A. Sengupta and the
speaker. We will explain how the distribution of the eigenvalues of a
large random unitary matrix taken under the heat kernel measure at a given
time can be expressed in purely combinatorial terms in function of walks
on the symmetric group. This relation between quantities defined on the
unitary and symmetric groups can be seen analytically as a consequence of
Ito\'s formula, or algebraically as an aspect of Schur-Weyl duality.
