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. ‏האירוע הזה כולל שיחת וידאו ב-Google Hangouts. הצטרף: https://hangouts.google.com/hangouts/_/mail.huji.ac.il/condensed?hceid=b...