Probability and Mathematical Physics Seminar

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Two point processes on the unit circle with non-local interactions

Speaker: Christophe Charlier, Lund University

Location: Warren Weaver Hall 1302

Date: Friday, March 10, 2023, 12:10 p.m.

Synopsis:

In this talk I will present results on two new point processes on the unit circle. At first sight, these point processes look similar to the well-studied circular-\beta-ensemble, but in fact there are very different: instead of featuring the 2d Coulomb interactions ~|e^{i\theta_j} - e^{i\theta_k}|^\beta, they are characterized by the non-local interactions ~|e^{i\theta_j} - e^{-i\theta_k}|^\beta and ~|e^{i\theta_j} + e^{i\theta_k}|^\beta, respectively. These point processes can be seen as \beta-ensembles of a new kind with a lot more randomness than in the classical \beta-ensembles. I will mostly be discussing the smooth linear statistics.