Geometric Structures seminar - Andrea Rosana - May 5, 2022 - 2:00 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All,

This is a reminder of today's seminar from the series "Geometric Structures".

Speaker: Andrea Rosana<https://www.math.sissa.it/users/andrea-rosana> (SISSA)
Title: Equilibrium measures and logarithmic potential theory (Part 2 of 2)

Time: May 5, 2022, 2:00 pm (Rome Time)
Venue: room 134
on zoom at this link:
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry

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Abstract:
We introduce the probability measure associated to the zeroes of Hermite polynomials and discuss how a rescaling is necessary in order to get convergence (in the weak star topology). Using the tools from logarithmic potential theory from previous talk, we show convergence of this measure to the semi-circular law. We then introduce Gaussian Ensambles and the empirical and statistical eigenvalue distributions for hermitian matrices in these ensambles. We show how these ensambles fit in a more general framework and we discuss the generalized Wigner theorem, highlighting a parallelism with Laplace asymptotic method. From this we get as a corollary the convergence of the (rescaled) statistical eigenvalue distribution for GOE matrices to the semi-circular law.


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More information can be found here: https://sites.google.com/view/geometric-structures/
Everyone is welcome!


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Miruna-Stefana Sorea
Postdoctoral Researcher
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
https://sites.google.com/view/mirunastefanasorea/