Correlation inequalities and the symmetric exclusion processes over general graphs

Speaker: Roberto Imbuzeiro

Affiliation: IMPA, Brazil

Abstract:

In a k-particle symmetric exclusion process over graph G, k unlabelled particles occupy distinct vertices of G. Particle jumps between adjacent vertices happen at rate 1, except that jumps to occupied sites are supressed. While this process is relatively well understood over G=Zd, (Z/nZ)d or nice subgraphs of them, not much is known about it over general graphs. In this talk we develop some tools that relate the exclusion process over G to a regular continuous-time random walk over G. In particular, we prove a correlation inequality for hitting "moving tagets": if k particles move according to the exclusion rule, they are at least as likely to hit an independently evolving set by time t as k independent walkers. We then use these results to obtain general bounds on the mixing time of symmetric exclusion in terms of the spectral gap of G. [Work in progress.]