Special Probability Seminar

Room: TBD

The speaker will talk about the infinite particle limit of eigenvalue stochastic dynamics introduced in the mathematics literature by Rider and Valko, and also studied in statistical physics by Grabsch-Texier and Bouchaud-Gautie-Le Doussal. These are the canonical dynamics associated to the inverse Laguerre ensemble in the way Dyson Brownian motion is related to the Gaussian ensemble. For the model of Rider-Valko we can prove convergence, from all initial conditions, to a new infinite-dimensional Feller process, describe the limiting dynamics in terms of an infinite system of log-interacting SDE that is out-of-equilibrium and finally show convergence in the long-time limit to the equilibrium state given by the (inverse points of the) Bessel determinantal point process. Time permitting the speaker will discuss some work in progress. This is joint work with Zahra Sadat Mirsajjadi.