Probability Seminar: Difference between revisions
(Replaced content with "__NOTOC__ Back to Probability Group Past Seminars = Spring 2024 = <b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b> We usually end for questions at 3:20 PM. == January 25, 2024: Tatyana Shcherbina (UW-Madison) == '''TBA'''") Tag: Replaced |
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== January 25, 2024: Tatyana Shcherbina (UW-Madison) == | == January 25, 2024: Tatyana Shcherbina (UW-Madison) == | ||
'''TBA''' | '''TBA''' | ||
== February 1, 2024: [https://lopat.to/index.html Patrick Lopatto (Brown)] == | |||
'''Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices''' | |||
We consider two related questions about the extremal statistics of Wigner matrices (random symmetric matrices with independent entries). First, how much can their eigenvalues fluctuate? It is known that the eigenvalues of such matrices display repulsive interactions, which confine them near deterministic locations. We provide optimal estimates for this “rigidity” phenomenon. Second, what is the behavior of the maximum of the characteristic polynomial? This is motivated by a conjecture of Fyodorov–Hiary–Keating on the maxima of logarithmically correlated fields, and we will present the first results on this question for Wigner matrices. This talk is based on joint work with Paul Bourgade and Ofer Zeitouni. | |||
Revision as of 17:14, 3 January 2024
Spring 2024
Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom
We usually end for questions at 3:20 PM.
January 25, 2024: Tatyana Shcherbina (UW-Madison)
TBA
February 1, 2024: Patrick Lopatto (Brown)
Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices
We consider two related questions about the extremal statistics of Wigner matrices (random symmetric matrices with independent entries). First, how much can their eigenvalues fluctuate? It is known that the eigenvalues of such matrices display repulsive interactions, which confine them near deterministic locations. We provide optimal estimates for this “rigidity” phenomenon. Second, what is the behavior of the maximum of the characteristic polynomial? This is motivated by a conjecture of Fyodorov–Hiary–Keating on the maxima of logarithmically correlated fields, and we will present the first results on this question for Wigner matrices. This talk is based on joint work with Paul Bourgade and Ofer Zeitouni.