Random matrices and simulation of Coulomb gases

• Grant number: 23/02674-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2023
• End date: May 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Guilherme Lima Ferreira da Silva
• Grantee: João Victor Alcântara Pimenta
• 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

The study of Random Matrices connects to a diverse range of areas, for instance to statistical mechanics and, of particular relevance for us, to the modeling of gases. By studying the spectral density of Gaussian-type random matrices, one can develop the simulation of Coulomb gas systems. Some difficulties arise in implementing simulations based on this theory, mainly in system scalability and the treatment of possible singularities. To solve these problems, the literature has simulated these gases, with excellent numerical behavior, using the Monte Carlo Hybrid Algorithm. We wish to explore this problem, the simulations, and the proposed algorithm along with extending the potentials to which it has been tested in the literature.