Mikhail Tikhonov
University of Virginia
Title
Noncolliding q-exchangeable random walks
Abstract
This talk is about a system of noncolliding q-exchangeable random walks on the set of nonnegative integers making steps straight or down from some initial configuration. Following Gnedin and Olshanski, we say that a (single) simple random walk is called a q-exchangeable random walk if, under an elementary transposition of the neighboring steps, the probability of the trajectory is multiplied by a parameter q in the unit interval [0, 1]. Our process of m noncolliding q-exchangeable random walks is obtained from the independent q-exchangeable walks via Doob's h-transform. We show that the trajectory forms a determinantal point process and obtain its kernel, limit shape, and local statistics. The work is based on joint research (arXiv:2303.02380) with L. Petrov.