MIXING OF THE SYMMETRIC EXCLUSION PROCESSES IN TERMS OF THE CORRESPONDING SINGLE-PARTICLE RANDOM WALK

• 成果类型: Article
• 署名作者: Oliveira, Roberto Imbuzeiro
• 署名单位: Instituto Nacional de Matematica Pura e Aplicada (IMPA)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP714
• 发表日期: 2013
• 页码: 871-913
• 关键词: logarithmic sobolev inequality; spectral gap; time; percolation; cluster; bounds

摘要

We prove an upper bound for the epsilon-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to T-RW(G) ln(vertical bar V vertical bar/epsilon), where vertical bar V vertical bar is the number of vertices in G, and T-RW(G) is the 1/4-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clusters, the giant component of the Erdos-Renyi random graph and Poisson point processes in R-d. Our technical tools include a variant of Morris's chameleon process.