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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.07999 |
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| _version_ | 1866909073970036736 |
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| author | Tsegaye, Eyob |
| author_facet | Tsegaye, Eyob |
| contents | 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 $\frac{1}{2kπ^2}N^2\log m$. 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 $\frac{1}{2kπ^2}N^2\log (kN)$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixing Time and Cutoff for the k-SEP Tsegaye, Eyob Probability Mathematical Physics 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 $\frac{1}{2kπ^2}N^2\log m$. 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 $\frac{1}{2kπ^2}N^2\log (kN)$. 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. |
| title | Mixing Time and Cutoff for the k-SEP |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2401.07999 |