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Rigidity of eigenvalues for beta ensemble in multi-cut regime

Date: Thursday, October 4, 2018 16:00 - 18:00
Speaker: Yiting Li (KTH Stockholm)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Laszlo Erdös
Contact: Susanne Wheatley
Lab building west seminar room

Abstract:

I will first talk about the background and some well known results of beta ensemble. Then I will introduce the rigidity of eigenvalues for beta ensemble in multi-cut regime, i.e., the fact that each eigenvalue in the bulk is very close to its "classical location". The probability that the distance between the eigenvalue and its classical location is larger than N^{-1+r} is exponentially small where r is an arbitrarily small positive number. The model is an generalization of the beta ensemble in one-cut regime for which the rigidity of eigenvalues was proved by Bourgade, Erdos and Yau. Finally I will explain the difference between the proof in one-cut case and the proof in multi-cut case.

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