Mixing times for the TASEP on the circle
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866918288589586432 |
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| author | Schmid, Dominik Sly, Allan |
| author_facet | Schmid, Dominik Sly, Allan |
| contents | We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a circle of length $N$ with $k$ particles. We show that the mixing time is of order $N^2 \min(k,N-k)^{-1/2}$, and that the cutoff phenomenon does not occur. This confirms behavior which was separately predicted by Jara, Lacoin and Peres, and it is more broadly believed to hold for integrable models in the KPZ-universalty class. Our arguments rely on a connection to periodic last passage percolation with a detailed analysis of flat geodesics, as well as a novel random extension and time shift argument for last passage percolation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_11896 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mixing times for the TASEP on the circle Schmid, Dominik Sly, Allan Probability Mathematical Physics 60K35, 60K37, 60J27 We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a circle of length $N$ with $k$ particles. We show that the mixing time is of order $N^2 \min(k,N-k)^{-1/2}$, and that the cutoff phenomenon does not occur. This confirms behavior which was separately predicted by Jara, Lacoin and Peres, and it is more broadly believed to hold for integrable models in the KPZ-universalty class. Our arguments rely on a connection to periodic last passage percolation with a detailed analysis of flat geodesics, as well as a novel random extension and time shift argument for last passage percolation. |
| title | Mixing times for the TASEP on the circle |
| topic | Probability Mathematical Physics 60K35, 60K37, 60J27 |
| url | https://arxiv.org/abs/2203.11896 |