Lecturer: Prof. Uzy Smilansky
Affiliation: Department of Physics of Complex
Systems, Weizmann Institute of Science
Abstract:
In his 1962 paper, F. Dyson introduced a then
novel approach for the study of random matrix
ensembles in terms of Brownian dynamics in
the space of matrices. He then proposed a
Fokker-Planck evolution for the spectral
distribution function, whose stationary solution
provides the ensemble's spectral joint
probability distribution function
$P(\lambda_1,\cdots,\lambda_N)$. Here, we
reformulate the approach for the traces $t_n =
\sum_{k=1}^{N} \lambda_k^n$, and derive the
corresponding Fokker-Planck equations and
the joint probability distribution
$Q(t_1,\cdots,t_N)$. The advantages of this
version of Dyson's theory will be discussed, and
a few new identities between traces will be
derived.