Non-intersecting paths in the plane, loop-erased walks and random matrices.

Resumen:  Non-intersecting processes in one dimension have long been an integral part of random matrix theory, at least since the pioneering work of F. Dyson in the 1960s. For planar (two-dimensional) state space processes, it is not clear how to generalize these connections since the paths under consideration are allowed to have self-intersections (or loops). In this talk, we address this problem and consider systems of random walks in planar graphs constrained to a certain type of non-intersection involving their loop-erased parts (this is closely related to connectivity probabilities of branches of the uniform spanning tree). We show that in a suitable scaling limit in terms of independent planar Brownian motions, certain exist distributions also have connections with random matrices, mainly Cauchy-type and circular ensembles. This is joint work with Neil O’Connell.

Date: Jun 09, 2021 at 16:16:00 h
Venue: Modalidad Vía Online.
Speaker: Jonas Arista
Affiliation: Universidad de Chile- CMM
Coordinator: Avelio Sepúlveda
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Posted on Jun 7, 2021 in Seminario Probabilidades CMM, Seminars