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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2412.03370 |
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| _version_ | 1866911170139521024 |
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| author | Gernholt, Sabrina |
| author_facet | Gernholt, Sabrina |
| contents | We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with a general initial condition and a deterministically moving wall in front of the particles. Using colour-position symmetry, we express the one-point distributions in terms of particle positions in a TASEP with step initial condition along a space-like path.
Based on this formula, we analyse the large-time asymptotics of the model under various scenarios. For initial conditions other than the step initial condition, we identify a distinct asymptotic behaviour at the boundary of the region influenced by the wall, differing from the observations made in [Borodin-Bufetov-Ferrari'24] and [Ferrari-Gernholt'24]. Furthermore, we demonstrate that product limit distributions are associated with shocks in the macroscopic empirical density.
As a special case of our starting formula, we derive a variational expression for the one-point distributions of TASEP with arbitrary initial data. Focusing on non-random initial conditions, such as periodic ones with an arbitrary density, we leverage our analytical tools to characterise the limit distribution within the framework of particle positions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | TASEP with a general initial condition and a deterministically moving wall Gernholt, Sabrina Probability Mathematical Physics We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with a general initial condition and a deterministically moving wall in front of the particles. Using colour-position symmetry, we express the one-point distributions in terms of particle positions in a TASEP with step initial condition along a space-like path. Based on this formula, we analyse the large-time asymptotics of the model under various scenarios. For initial conditions other than the step initial condition, we identify a distinct asymptotic behaviour at the boundary of the region influenced by the wall, differing from the observations made in [Borodin-Bufetov-Ferrari'24] and [Ferrari-Gernholt'24]. Furthermore, we demonstrate that product limit distributions are associated with shocks in the macroscopic empirical density. As a special case of our starting formula, we derive a variational expression for the one-point distributions of TASEP with arbitrary initial data. Focusing on non-random initial conditions, such as periodic ones with an arbitrary density, we leverage our analytical tools to characterise the limit distribution within the framework of particle positions. |
| title | TASEP with a general initial condition and a deterministically moving wall |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2412.03370 |