Student Probability Seminar

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Optimal local law and central limit theorem for \beta-ensembles

Speaker: Krishnan Mody, CIMS

Location: Warren Weaver Hall 517

Date: Monday, November 1, 2021, 11:30 a.m.

Synopsis:

In this talk I will first outline the proof of the optimal local law for \beta-ensembles, focusing on the Gaussian case to highlight the main idea. I will then talk about how this helps to establish

1) The optimal rigidity of eigenvalues,  
2) the log-correlated structure for the log-characteristic-polynomial, the imaginary part of which controls the joint fluctuations of eigenvalues.