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Mixing of the Exclusion Process with Small Bias

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Abstract

We analyze the mixing behavior of the biased exclusion process on a path of length n as the bias \(\beta _n\) tends to 0 as \(n \rightarrow \infty \). We show that the sequence of chains has a pre-cutoff, and interpolates between the unbiased exclusion and the process with constant bias. As the bias increases, the mixing time undergoes two phase transitions: one when \(\beta _n\) is of order 1 / n, and the other when \(\beta _n\) is order \(\log n/n\).

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Acknowledgements

We thank Perla Sousi and Nayantara Bhatnagar for helpful comments on an earlier version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Fenton Hall, University of Oregon, Eugene, OR, 97403-1222, USA

    David A. Levin

  2. Microsoft Research, 1 Microsoft Way, Redmond, WA, 98052, USA

    Yuval Peres

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  1. David A. Levin
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  2. Yuval Peres
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Correspondence to David A. Levin.

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Levin, D.A., Peres, Y. Mixing of the Exclusion Process with Small Bias. J Stat Phys 165, 1036–1050 (2016). https://doi.org/10.1007/s10955-016-1664-z

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  • DOI: https://doi.org/10.1007/s10955-016-1664-z

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