On the percolation threshold of the contact process with stirring

• Grant number: 25/02707-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2025
• End date: May 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Leonardo Trivellato Rolla
• Grantee: Jhon Kevin Astoquillca Aguilar
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

The aim of this project focuses on the study of the stationary measures of the contact process with stirring on the Euclidean lattice. In this model, particles placed on the lattice follow the birth-and-death dynamic as the contact process and interchange their locations or move to a new location as the exclusion process dynamic. We refer to this rate of occurrence as the stirring parameter. Fixing the stirring parameter, we aim to study the percolation properties of configurations sampled from the stationary measures of this model with a particular focus on the phase transition regarding the existence of an infinite connected set of particles as the parameter of infection of the contact process dynamic is varied. The second part of the project is to compare this critical parameter for percolation with the parameter of survival of particles to obtain that they are different when the stirring parameter is large, thus making some progress in the open question, which asks whether these critical parameters coincide in, dimensions greater than 2 for the standard contact process. (AU)