Asymptotic analysis for a model of products of coupled random matrices with arbitrary polynomial potential

• Grant number: 20/15699-3
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2021
• End date: January 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Guilherme Lima Ferreira da Silva
• Grantee: Caio Eduardo Candido
• 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

Abstract

Singular values of products of random matrices appear in a wide range of areas in Science, from dynamical systems, High Energy Physics, statistical analysis to telecommunications, to mention only a few. Despite its interest, the rigorous analysis was limited to models of independent random matrices until very recently, when several case-studies for a coupled model of random matrices started to appear. This doctoral research proposal focuses on the investigation of a class of models, which includes several of these case-studies as particular cases, with the main goal of carrying out the asymptotic analysis of it. This way, we expect to obtain several limiting processes for the singular values, under various scaling regimes. (AU)