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Relaxation times are stationary hitting times of large sets

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arxiv 2304.05878 v1 pith:7QA6PFYH submitted 2023-04-12 math.PR

Jonathan Hermon This is my paper · ORCID
classification math.PR
keywords timescharacterizationhittinglargesetsstationaryexpectedgive
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We give a characterization of the relaxation time up to an absolute constant factor, in terms of stationary expected hitting times of large sets. This resolves a conjecture of Aldous and Fill. We give a similar characterization for the spectral profile. We also provide in the non-reversible setup a related characterization for stationary expected hitting times of large sets.

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  1. One- and two-particle spectral gap identities for the symmetric inclusion process and related models

    math.PR 2024-12 accept novelty 7.0 of 10

    In the small-diffusivity limit, the spectral gap of the symmetric inclusion process with any number of particles equals that of the two-particle process, while adding reservoirs restores the one-particle random walk identity.

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