Limiting Theorems for Eigenvalues of Random Matrices

• Grant number: 21/09348-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2021
• End date: September 30, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Guilherme Lima Ferreira da Silva
• Grantee: Ester Beatriz de Souza dos Santos
• 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

This undergraduate research project aims at introducing the students on basic results in random matrix theory. The student will learn basic questions in random matrix theory and how to interpret them with the help of computational simulation. She should also understand the proofs of the Semicircle Law and the Tracy-Widom distribution for the eigenvalues of the Gaussian Unitary ensemble.