I 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 I will discuss some work in progress. This is joint work with Zahra Sadat Mirsajjadi.