Brownian Motion in Gaussian Ensembles Formalism - General Treatment and Thermodynamics

In this seminar talk we present the Dyson's ideas to generalize the notion of a matrix ensemble in such a way that the Coulomb gas model acquires meaning not only as a static model in timeless thermodynamical equilibrium but as a dynamical system that may be in an arbitrary nonequilibrium state changing with time. In addition to this we revisited some ideas and properties of circular ensembles to, finally, find the thermodynamical observables of a Dyson gas.