Abstract: The talk is about two types of interacting particle systems related to the classical ensembles of random matrices. The prototypical examples are Dyson Brownian motion (also called non-intersecting Brownian motions) and Brownian TASEP (also called Brownian motions with one-sided collisions/reflections) respectively. I will discuss explicit formulae for their distributions, their correlation functions and some non-trivial connections between the two types of interacting particle systems. The bulk of the talk will be mainly focussed on surveying results for the Gaussian/Brownian case.
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