Geometric Structures seminar - Andrea Rosana - April 28, 2022 - 2:00 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All,

This is to announce the next 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 1 of 2)

Time:          April 28, 2022, 2:00 pm (Rome Time)



Venue - hybrid:

  *   at room 134 at SISSA
  *
  *   from remote, on zoom at this link

https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry

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Abstract:
The aim of these talks is to show that the (rescaled) zeroes of Hermite polynomials and the (rescaled) eigenvalues of matrices in the Gaussian Orthogonal Ensemble share the same asymptotic distribution, i.e. the semi-circle law of radius \sqrt(2). We address this problem through logarithmic potential theory.

We begin by showing how we can interpret the zeroes of orthogonal polynomials as equilibrium configurations for the electrostatic Stieltjes model on the real line, which serves as a motivation for their study. We then introduce logarithmic potential and energy of a measure with respect to an external potential. Under suitable hypothesis on such potential, we show the existence and uniqueness of a minimizing measure for the energy, which we call the equilibrium measure. A characterization of such equilibrium measures is also provided. We end the talk briefly discussing the equilibrium measure for a Gaussian potential.

The tools we developed here will be used in the second talk to address our starting problem.
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More information can be found here: https://sites.google.com/view/geometric-structures/

Everyone is welcome!



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