Scaling limit of condensed zero range processes

• Grant number: 19/02226-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2019
• End date: August 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Luiz Renato Gonçalves Fontes
• Grantee: Tiecheng Xu
• 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

This project is devoted to the study of long time behavior of the condensed zero rangeprocesses. There have been a large number of research on the zero range process with infinitecritical density. However for the process with finite critical density, not so much is known. Thecondensed zero range process, as a model of latter type, has a very interesting feature: starting from a super-critical initial density profile, a large portion of particles tend to accumulate at some single site. In this project we mainly focus on three problems aboutthe scaling limit of condensed zero range processes: (1) metastability in phase transition. Wewould like to describe the time evolution of the site which contains most of the particles. Thereversible case with ± > 1 has been solved. The condensation phenomenon does notoccur for ± < 1. We plan to investigate the reversible case with ± = 1; (2) hydrodynamiclimit. We plan to deduce the hydrodynamic limit of the condensed zero range process withsuper-critical initial profile; (3) spectral gap. We will try to obtain a sharp estimate on th espectral gap of the condensed zero range process for ± e 1. (AU)