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:  Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences 
Depositing User:  Richard Pymar 
Date Deposited:  26 Jun 2020 05:04 
Last Modified:  09 Aug 2023 12:47 
URI:  https://eprints.bbk.ac.uk/id/eprint/30561 
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