### Infinite-dimensional diffusions from random matrix dynamics

Probability Seminar

27th September 2024, 3:30 pm – 4:30 pm

Fry Building, 2.04

I will talk about the infinite particle limit of eigenvalue stochastic dynamics introduced by Rider and Valko. These are the canonical dynamics associated to the inverse Laguerre ensemble in the way Dyson Brownian motion is related to the Gaussian ensemble. For this model 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.

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