Communities in random graphs and other complex structures

• Grant number: 24/12778-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: May 01, 2025
• End date: April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Florencia Graciela Leonardi
• Grantee: Florencia Graciela Leonardi
• Visiting researcher: Maria Ines Armendariz
• Visiting researcher institution: Universidad De Buenos Aires/Uba , Argentina
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• City of the host institution: São Paulo
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

In this project, we propose to study three problems. The first two are related to the identification of hidden variables, such as communities or block partitions of a set of nodes, from the observation of an additional structure. For the stochastic block model, we will rigorously study a very natural method based on the harmonic functions of a graph with connection probabilities determined by the community organization. We also propose to infer the blocks in the Ising model from the observation of a Markov chain on the set of nodes that leaves the Gibbs distribution invariant. These are joint projects with Andressa Cerqueira (UFSCAR), Florencia Leonardi (USP), Nancy Lopes Garcia (UNICAMP) and Nicolás Agote (Universit\'e Toulouse III and Universidad de Buenos Aires). The third problem is to study the local fluctuations of contingency tables with macroscopic profiles. This is a collaboration with Luiz Renato Fontes (USP) and Pablo A. Ferrari (UBA). (AU)