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)

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

XU, TIECHENG. Condensation of the Invariant Measures of the Supercritical Zero Range Processes. Journal of Statistical Physics, v. 191, n. 6, p. 18-pg., 2024-06-14. (19/02226-2)