| Grant number: | 19/16062-1 |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| Start date: | March 01, 2020 |
| End date: | February 28, 2026 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal Investigator: | Guilherme Lima Ferreira da Silva |
| Grantee: | Guilherme Lima Ferreira da Silva |
| Host Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
| City of the host institution: | São Carlos |
| Associated researchers: | Daniel Ungaretti Borges ; Igor Mencattini ; Lun Zhang ; Maxym Yattselev ; Thaís Jordão |
| Associated research grant(s): | 25/17465-3 - Riemann-Hilbert methods and the Six-Vertex Model, AP.R |
| Associated scholarship(s): | 24/06997-1 - Asymptotics of Partition Functions of Coulomb Gases,
BP.MS 23/10533-8 - Deformations of orthogonal polynomials and integro-differential Painlevé equations, BP.PD 23/06150-6 - Brownian Motion and Markov Chains, BP.IC + associated scholarships - associated scholarships |
Abstract
In recent years random matrices have found applications in a vast number of different areas of science, such as telecommunications, high energy physics, number theory, machine learning, big data, dynamical systems, differential equations, computer science, among several others. The connection with interacting particle systems becomes natural when one asks questions about eigenvalues of large random matrices. Typically, such random eigenvalues interact with one another in a repulsive way, mimicking the interactions of several different and seemingly unrelated models from both equilibrium and non-equilibrium systems. Thus, one of the fundamental questions is to understand how the eigenvalues of a given large random matrix behave in different scaling regimes. This project proposes to explore several different facets of eigenvalues of large random matrices and other interacting particle systems. We will study how the thermodynamic limit of different interacting particle systems can be understood in terms of equilibrium problems on the plane, and use this information to carry out the asymptotic analysis of the models of interest, also expecting to unravel novel striking connections with integrable systems. (AU)
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