Large deviation principle for the stationary measures of open asymmetric simple exclusion processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915068727263232 |
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| author | Hegde, Milind Yang, Zongrui |
| author_facet | Hegde, Milind Yang, Zongrui |
| contents | We consider the stationary measure of the asymmetric simple exclusion process (ASEP) on a finite interval in $\mathbb{Z}$ with open boundaries. Fixing all the jump rates and letting the system size approach infinity, the height profile of such a sequence of stationary measures satisfies a large deviation principle (LDP), whose rate function was predicted in the physics work arXiv:cond-mat/0205353. In this paper, we provide the first rigorous proof of the large deviation principle in the "fan region" part of the phase diagram. Our proof relies on two key ingredients: a two-layer expression of the stationary measure of open ASEP, arising from the Enaud-Derrida representation arXiv:cond-mat/0307023 of the matrix product ansatz, and the large deviation principle of the open totally asymmetric simple exclusion process (TASEP) recently established in arXiv:2403.03275. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12026 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviation principle for the stationary measures of open asymmetric simple exclusion processes Hegde, Milind Yang, Zongrui Probability We consider the stationary measure of the asymmetric simple exclusion process (ASEP) on a finite interval in $\mathbb{Z}$ with open boundaries. Fixing all the jump rates and letting the system size approach infinity, the height profile of such a sequence of stationary measures satisfies a large deviation principle (LDP), whose rate function was predicted in the physics work arXiv:cond-mat/0205353. In this paper, we provide the first rigorous proof of the large deviation principle in the "fan region" part of the phase diagram. Our proof relies on two key ingredients: a two-layer expression of the stationary measure of open ASEP, arising from the Enaud-Derrida representation arXiv:cond-mat/0307023 of the matrix product ansatz, and the large deviation principle of the open totally asymmetric simple exclusion process (TASEP) recently established in arXiv:2403.03275. |
| title | Large deviation principle for the stationary measures of open asymmetric simple exclusion processes |
| topic | Probability |
| url | https://arxiv.org/abs/2412.12026 |