Mixing Time and Cutoff for the k-SEP

2024/01/15 by Tsegaye, Eyob · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.07999

Abstract

We investigate the mixing time of the capacity k simple exclusion process (also called the partial exclusion process) of Schultz and Sandow with m particles on a segment of length N. We show that the k-SEP exhibits cutoff at time (1)/(2kπ²)N²log m. We also introduce a related complete multi-species process that we call the S_k,N shuffle and show that this process exhibits cutoff at time (1)/(2kπ²)N²log (kN). This extends the celebrated result of Lacoin which determined the mixing time of the symmetric simple exclusion process on a segment of length N and the adjacent transposition shuffle, and proved cutoff in both.

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• Point process convergence of extremes in K-symmetric exclusion

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