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Mixing time and cutoff for the k-SPEP

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  • Tsegaye, Eyob

Abstract

We investigate the mixing time of the capacity k symmetric partial exclusion process of Schütz and Sandow with m particles on a segment of length N, and we show that this process exhibits cutoff at time 12kπ2N2logm. We also introduce a related complete multi-species process that we call the Sk,N shuffle and show that this process exhibits cutoff at time 12kπ2N2log(N). This extends the celebrated result of Lacoin, which proved cutoff for the symmetric simple exclusion process on a segment of length N and the adjacent transposition shuffle.

Suggested Citation

  • Tsegaye, Eyob, 2026. "Mixing time and cutoff for the k-SPEP," Stochastic Processes and their Applications, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002200
    DOI: 10.1016/j.spa.2025.104776
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    References listed on IDEAS

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    1. Franceschini, C. & Gonçalves, P. & Jara, M. & Salvador, B., 2024. "Non-equilibrium fluctuations for SEP(α) with open boundary," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    2. Floreani, Simone & Redig, Frank & Sau, Federico, 2021. "Hydrodynamics for the partial exclusion process in random environment," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 124-158.
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