TASEP in half-space
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912523980111872 |
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| author | Zhang, Xincheng |
| author_facet | Zhang, Xincheng |
| contents | In this work, we present the multi-point probability distribution of the totally asymmetric simple exclusion process (TASEP) in a half-space, starting from a general deterministic initial condition. More precisely, let $h(t,x)$ denote the height function of TASEP at position $x$ and time $t$; we provide an explicit formula for \begin{equation*} \mathbb{P}(h(t,y_1)\leq s_1, \ldots, h(t,y_m)\leq s_m). \end{equation*} The formula presented is well-suited for the scaling limit analysis. By applying a 1:2:3 scaling, we derive the probability distribution for the half-space KPZ fixed point, which is conjectured to be the universal process for the limit of the KPZ universality models restricted to a half-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | TASEP in half-space Zhang, Xincheng Probability Mathematical Physics 60J74 In this work, we present the multi-point probability distribution of the totally asymmetric simple exclusion process (TASEP) in a half-space, starting from a general deterministic initial condition. More precisely, let $h(t,x)$ denote the height function of TASEP at position $x$ and time $t$; we provide an explicit formula for \begin{equation*} \mathbb{P}(h(t,y_1)\leq s_1, \ldots, h(t,y_m)\leq s_m). \end{equation*} The formula presented is well-suited for the scaling limit analysis. By applying a 1:2:3 scaling, we derive the probability distribution for the half-space KPZ fixed point, which is conjectured to be the universal process for the limit of the KPZ universality models restricted to a half-space. |
| title | TASEP in half-space |
| topic | Probability Mathematical Physics 60J74 |
| url | https://arxiv.org/abs/2409.09974 |