I wil l first talk about the background and some well known results of beta ense mble. 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 t he distance between the eigenvalue and its classical location is larger th an N^{-1+r} is exponentially small where r is an arbitrarily small positiv e number. The model is an generalization of the beta ensemble in one-cut r egime for which the rigidity of eigenvalues was proved by Bourgade\, Erdos and Yau. Finally I will explain the difference between the proof in one-c ut case and the proof in multi-cut case.

LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS T Austria ORGANIZER:jdeanton@ist.ac.at SUMMARY:Rigidity of eigenvalues for beta ensemble in multi-cut regime URL:https://talks-calendar.app.ist.ac.at/events/1398 END:VEVENT END:VCALENDAR