Mathematical Physics seminar at SISSA

[Tamara Grava]

Dear all

a gentle reminder of  this week  Mathematical Physics seminar


Wednesday the 31st of May at 4.00pm room 132

Speaker: Giorgio Cipolloni (Princeton Center for Theoretical Science, USA)

Title: How do the eigenvalues of a large non-Hermitian random matrix behave?

Abstract: We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a non-natural scale, due to strong correlations between the eigenvalues.
Then, motivated by the long time behaviour of the ODE \dot{u}=Xu, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X.



Wednesday the 7th of June  at 4.00pm room 132

Speaker: Guido Mazzuca (KTH, Sweden)
Title: LARGE DEVIATION PRINCIPLE FOR THE ABLOWITZ-LADIK LATTICE AND THE CIRCULAR β ENSEMBLE AT HIGH TEMPERATURE

Abstract: This presentation delves into the fascinating relationship between integrable systems theory and random matrix theory. In particular, a method to calculate the eigenvalue density of the Lax matrix   of the Ablowitz-Ladik lattice   sampled from the  Generalized Gibbs ensemble is derived.  This characterization is achieved by employing a large deviation principle (LDP). Additionally,  a connection between this LDP and the one of the Circular β ensemble in the high temperature regime is established. This permits to  explicitly compute the eigenvalue density of the Ablowitz-Ladik lattice random Lax matrix.

Wednesday the 14th of June  at 4.00pm room 132

Speaker: Marco Bertola (Concordia University, Montreal)
Title:TBA