Journée thématique autour des matrices aléatoires

Titres et résumés

1. About large deviations for the largest eigenvalue of random matrices

Alice Guionnet

09/04/2024 10:30

Large deviations for the largest eigenvalue of random matrices are useful for instance to study the complexity of random functions, in particular the volume of their minima. The simplest model could be studied by Auffinger-Ben Arous -Cerny by using large deviation for the largest eigenvalue of a Gaussian matrix. To include a signal, Ben Arous, Mei, Montanari and Nica used large deviations for...

3. Characteristic polynomial outside of the support

David García-Zelada

09/04/2024 11:45

When taking a sequence of random polynomials with independent coefficients, there may remain zeros outside of the limiting support, and the behavior of these zeros depends on the law of its coefficients.
After recalling this fact, we will see that this does not happen when the random polynomials arise as the characteristic polynomials of a family of non-Hermitian random matrices.
Moreover,...

2. Zeros of conditional Gaussian analytic functions, random sub-unitary matrices and q-series

Boris Khoruzhenko

09/04/2024 14:00

I will talk about zeros of the infinite Gaussian power series $f(z)=\sum c_k z^k$ conditioned on the event that $f(0)=a$. Forrester and Ipsen 2019 showed that if the coefficients $c_k$ are independent standard complex normals then the conditional probability law of the zero set of $f(z)$ can be obtained from that of the spectrum of random subunitary matrices. I will explain how using this...

4. On the density of complex eigenvalues of sub-unitary scattering matrices.

Yan Fyodorov

09/04/2024 15:15

What is the density of eigenvalues for a finite-size diagonal block of a resolvent of a large random matrix, with the spectral parameter chosen in the vicinity of the real axis?
I will explain how this mathematical question is motivated by real experiments in wave-scattering systems, where due to absorption the associated scattering matrix is sub-unitary, hence moduli of its eigenvalues are...