Pymar, Richard and Hermon, J. (2020) The exclusion process mixes (almost) faster than independent particles. Annals of Probability 48 (6), pp. 3077-3123. ISSN 0091-1798.
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Abstract
Oliveira conjectured that the order of the mixing time of the exclusion process with k-particles on an arbitrary n-vertex graph is at most that of the mixing-time of k independent particles. We verify this up to a constant factor for d-regular graphs when each edge rings at rate 1/d in various cases: (1) when d = Ω(logn/k n), (2) when gap := the spectral-gap 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 spectral-gap 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 vertex-transitive graphs of moderate growth and for supercritical percolation on a fixed dimensional torus.
Metadata
| Item Type: | Article |
|---|---|
| Keyword(s) / Subject(s): | Exclusion process, mixing-time, 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: | 12 Apr 2025 05:28 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/30561 |
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