Probability Seminar: Difference between revisions
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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. | 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. | ||
== February 8, 2024: TBA == | |||
'''TBA''' | |||
== February 15, 2024: Brian Rider (Temple) == | |||
'''TBA''' | |||
== February 22, 2024: TBA == | |||
'''TBA''' | |||
== February 29, 2024: TBA == | |||
'''TBA''' | |||
== March 7, 2024: Atilla Yilmaz (Temple) == | |||
'''TBA''' | |||
== March 14, 2024: Eric Foxall (UBC Okanagan) == | |||
'''TBA''' | |||
== March 21, 2024: Semon Rezchikov (Princeton) == | |||
'''TBA''' | |||
== March 28, 2024: Spring Break == | |||
'''TBA''' | |||
== April 4, 2024: TBA == | |||
'''TBA''' | |||
== April 11, 2024: Bjoern Bringman (Princeton) == | |||
'''TBA''' | |||
== April 18, 2024: TBA == | |||
'''TBA''' | |||
== April 25, 2024: Colin McSwiggen (NYU) == | |||
'''TBA''' | |||
== May 2, 2024: TBA == | |||
'''TBA''' | |||
Revision as of 20:12, 17 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.
February 8, 2024: TBA
TBA
February 15, 2024: Brian Rider (Temple)
TBA
February 22, 2024: TBA
TBA
February 29, 2024: TBA
TBA
March 7, 2024: Atilla Yilmaz (Temple)
TBA
March 14, 2024: Eric Foxall (UBC Okanagan)
TBA
March 21, 2024: Semon Rezchikov (Princeton)
TBA
March 28, 2024: Spring Break
TBA
April 4, 2024: TBA
TBA
April 11, 2024: Bjoern Bringman (Princeton)
TBA
April 18, 2024: TBA
TBA
April 25, 2024: Colin McSwiggen (NYU)
TBA
May 2, 2024: TBA
TBA