The exclusion process mixes (almost) faster than independent particles
Pymar, Richard and Hermon, J. (2020) The exclusion process mixes (almost) faster than independent particles. Annals of Probability 48 (6), pp. 30773123. ISSN 00911798.
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Abstract
Oliveira conjectured that the order of the mixing time of the exclusion process with kparticles on an arbitrary nvertex graph is at most that of the mixingtime of k independent particles. We verify this up to a constant factor for dregular graphs when each edge rings at rate 1/d in various cases: (1) when d = Ω(logn/k n), (2) when gap := the spectralgap of a single walk is O(1/ log4 n) and k > n Ω(1) , (3) when k ≍ n a for some constant 0 < a < 1. In these cases our analysis yields a probabilistic proof of a weaker version of Aldous’ famous spectralgap conjecture (resolved by Caputo et al.). We also prove a general bound of O(log n log log n/gap), which is within a log log n factor from Oliveira’s conjecture when k > n Ω(1). As applications we get new mixing bounds: (a) O(log n log log n) for expanders, (b) order d log(dk) for the hypercube {0, 1} d , (c) order (Diameter)2 log k for vertextransitive graphs of moderate growth and for supercritical percolation on a fixed dimensional torus.
Metadata
Item Type:  Article 

Keyword(s) / Subject(s):  Exclusion process, mixingtime, chameleon process, particle system 
School:  School of Business, Economics & Informatics > Economics, Mathematics and Statistics 
Depositing User:  Richard Pymar 
Date Deposited:  26 Jun 2020 05:04 
Last Modified:  14 Jun 2021 02:45 
URI:  https://eprints.bbk.ac.uk/id/eprint/30561 
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