Mixing time of particle systems and related processes

• Grant number: 23/12652-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2024
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Leonardo Trivellato Rolla
• Grantee: Shangjie Yang
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 17/10555-0 - Stochastic modeling of interacting systems, AP.TEM

Abstract

In this proejct, we first survey the topics about mixing time of heat-bath dynamics of interface models and particle systems of the following three models: random walk pinning models, metastablity of interface models, simple exclusion processes in a random environment. Furthermore, we state our contributions to these three models with a general picture and our innovations. Moreover, we ask some related further questions that we would like to pursue in the future, and state ongoing related research projects: (1) mixing time and spectral gap of the simple exclusion process and the interchange process in non-homogeneous conductances, (2) mixing time of the long range symmetric simple exclusion process on one-dimensional torus. Besides, we also mention two ongoing projects about random graph and Gaussian process in random environment respectively.