Mixing time and cutoff for the k-SPEP

Eyob Tsegaye

Stochastic Processes and their Applications, 2026, vol. 191, issue C

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.

Keywords: Markov chains; Mixing time; Exclusion process; Card shuffling; Cutoff phenomenon (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104776

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