Random Jacobi matrices

• Grant number: 20/02508-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2020
• End date: October 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Guilherme Lima Ferreira da Silva
• Grantee: Victor Julio Alves de Souza
• 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 interplay between orthogonal polynomials and the spectral theory of Jacobi operators can be considered as a classical, and yet very active nowadays, topic of research. Relatively more recent are the advances made in random matrix theory due greatly to the found connection with orthogonal polynomials. This M.D. proposal aims at studying these connections, and then combining the three topics together with a numerical and analytical study of random complex Jacobi matrices under the viewpoint of orthogonal polynomials. (AU)