Multiplicative Statistics for Orthogonal and Symplectic Ensembles

• Grant number: 23/01566-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2023
• End date: May 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Guilherme Lima Ferreira da Silva
• Grantee: Gabriel Passarelli
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 19/16062-1 - Asymptotic analysis of interacting particle systems and random matrix theory, AP.JP
• Associated scholarship(s): 24/09331-4 - Multiplicative statistics of Pfaffian Point Processes, BE.EP.MS

Abstract

Gap probabilities associated to point processes, and in particular to eigenvalues of random matrices, have been of great interest to the mathematical and physical communities in the past 20 years. In the past few years, more general multiplicative statistics came also to the spotlight, in much in virtue of uncovered connections to stochastic growth processes, in particular to the KPZ equation. This project aims at investigating some of these multiplicative statistics, for two classical random matrix models, namely the Gaussian orthogonal and symplectic ensembles.