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Probability and Combinatorics

Tuesday, November 30, 2021 - 3:30pm

Krishnan Mody

Courant Institute


Temple University

Wachman Hall 617

I will discuss recent work with P. Bourgade and M. Pain in which we show that the log-characteristic polynomial for general beta ensembles converges to a log-correlated field in the large-dimension limit. The proof of this result relies on a so-called optimal local law, which I will explain and prove in the Gaussian case. I will explain how the local law is useful, and give an outline of the proof of the log-correlated field.