Palestras e Seminários
27/03/2025
15:00
Sala 3-120
Modo: Presencial
Análise e Física Matemática
Abstract: This talk explores the connection between orthogonal polynomials and random matrices, with a focus on the Gaussian Unitary Ensemble (GUE). After introducing key notions and properties of orthogonal polynomials, I will examine how they arise in the study of random matrix models.
Building on results by Bleher and Deaño, I will discuss the effects of perturbations of the GUE and consider a model of orthogonal polynomials associated with a cubic potential. In this setting, the free energy admits a topological expansion related to graph enumeration on Riemann surfaces, with coefficients expressed through a solution of the Painlevé I equation.
I will also present recent results from a joint work with G. Silva (USP-ICMC) and M. Yattselev (Purdue University) on modifications of the measure in the cubic potential case. Our analysis yields an asymptotic expansion for the recurrence coefficients in inverse powers of $N^2$, revealing a connection with a perturbed Painlevé I equation.
