The TASEP on Galton-Watson trees
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arXiv
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| Format: | Preprint |
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2020
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| author | Gantert, Nina Georgiou, Nicos Schmid, Dominik |
| author_facet | Gantert, Nina Georgiou, Nicos Schmid, Dominik |
| contents | We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from $x$ to $y$ at rate $r_{x,y}$ provided $y$ is empty. Starting from the all empty initial condition, we show that the distribution of the configuration at time $t$ converges to an equilibrium. We study the current and give conditions on the transition rates such that the current is of linear order or such that there is zero current, i.e. the particles block each other. A key step, which is of independent interest, is to bound the first generation at which the particle trajectories of the first $n$ particles decouple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_10443 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The TASEP on Galton-Watson trees Gantert, Nina Georgiou, Nicos Schmid, Dominik Probability Mathematical Physics Primary: 60K35, Secondary: 60K37, 60J75, 82C20 We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from $x$ to $y$ at rate $r_{x,y}$ provided $y$ is empty. Starting from the all empty initial condition, we show that the distribution of the configuration at time $t$ converges to an equilibrium. We study the current and give conditions on the transition rates such that the current is of linear order or such that there is zero current, i.e. the particles block each other. A key step, which is of independent interest, is to bound the first generation at which the particle trajectories of the first $n$ particles decouple. |
| title | The TASEP on Galton-Watson trees |
| topic | Probability Mathematical Physics Primary: 60K35, Secondary: 60K37, 60J75, 82C20 |
| url | https://arxiv.org/abs/2008.10443 |