Student Probability Seminar

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Local Laws and a Mesoscopic CLT for beta ensembles

Speaker: Luke Peilen, CIMS

Location: Warren Weaver Hall 517

Date: Tuesday, September 20, 2022, 1 p.m.

Synopsis:

In this talk I’ll discuss the statistical mechanics of the log-gas, or beta- ensemble, for general potential and inverse temperature. I’ll focus on an electrostatic approach introduced by Sandier-Serfaty ‘15 for understanding the next order asymptotics, and discuss recent work on local energy control and fluctuations of linear statistics. I will show how one can use a bootstrap on scales to obtain local energy control down to an optimal logarithmic scale, and how one can use that associated control to understand the limiting behavior of the fluctuation measure.