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    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 , ISSN 0091-1798. (In Press)

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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 Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Richard Pymar
    Date Deposited: 26 Jun 2020 05:04
    Last Modified: 31 Jul 2020 05:54
    URI: http://eprints.bbk.ac.uk/id/eprint/30561

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