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Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement

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Abstract

This paper studies Markov chains on the chambers of real hyperplane arrangements, a model that generalizes famous examples, such as the Tsetlin library and riffle shuffles. We discuss cutoff for the Tsetlin library for general weights, and we give an exact formula for the separation distance for the hyperplane arrangement walk. We introduce lower bounds, which allow for the first time to study cutoff for hyperplane arrangement walks under certain conditions. Using similar techniques, we also prove a uniform lower bound for the mixing time of Glauber dynamics on a monotone system.

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Acknowledgements

I would like to thank Persi Diaconis, Balázs Gerencsér, Dan Jerison and Allan Sly for valuable communications.

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  1. Department of Mathematics, Princeton University, Princeton, USA

    Evita Nestoridi

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  1. Evita Nestoridi
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Correspondence to Evita Nestoridi.

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Nestoridi, E. Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement. Probab. Theory Relat. Fields 174, 929–943 (2019). https://doi.org/10.1007/s00440-018-0872-7

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  • DOI: https://doi.org/10.1007/s00440-018-0872-7

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