Multiplicative statistics of Pfaffian Point Processes

• Grant number: 24/09331-4
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: September 01, 2024
• End date: November 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Guilherme Lima Ferreira da Silva
• Grantee: Gabriel Passarelli
• Supervisor: Tom Claeys
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universitè Catolique de Louvain (UCL), Belgium
• Associated to the scholarship: 23/01566-0 - Multiplicative Statistics for Orthogonal and Symplectic Ensembles, BP.MS

Abstract

Pfaffian Point Processes are a class of point processes to which many fundamental models belong to, for instance, the Gaussian Orthogonal and the Gaussian Symplectic random matrix ensembles. The Pfaffian word stands for the fact that in these processes the statistics are written in terms of a Fredholm Pfaffian of an integral operator, which yields a natural setting for modeling strongly correlated point configurations. In this setting, interesting and relevant mathematical problems arise when we start to investigate multiplicative statistics. But not only that, in recent years, connections discovered between multiplicative statistics of point processes and celebrated growth models in mathematical physics prompted the interest on this type of problem. This BEPE project is situated in this context, having the purpose of introducing the student to recent investigations involving Pfaffian Point Processes, and of incorporating the student on an ongoing collaboration between the supervisor and host researcher.