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| Author(s): |
Gabriel Passarelli
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2025-07-14 |
| Examining board members: |
Guilherme Lima Ferreira da Silva;
Thomas Chouteau;
Tertuliano Franco Santos Franco;
Aline Duarte de Oliveira
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| Advisor: | Guilherme Lima Ferreira da Silva |
| Abstract | |
This work is an introduction to random matrix theory, with a focus on the invariant ensembles. It is presented in four main steps. First, we calculate the probability distribution induced on the eigenvalues by the distributions that define the invariant ensembles. Then, we introduce the language of point processes and study multiplicative statistics in each of these ensembles. After this, we discuss the concept of universality in random matrices and calculate the scaling limits for the GUE ensemble using the steepest descent method. Finally, motivated by its application in demonstrating the universality limits of invariant ensembles, we demonstrate an identity known as Widoms formula. (AU) | |
| FAPESP's process: | 23/01566-0 - Multiplicative Statistics for Orthogonal and Symplectic Ensembles |
| Grantee: | Gabriel Passarelli |
| Support Opportunities: | Scholarships in Brazil - Master |