The TASEP on Galton–Watson trees
- 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 rx,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.
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| Author: | Nina Gantert, Nicos Georgiou, Dominik SchmidGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1231384 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/123138 |
| ISSN: | 1083-6489OPAC |
| Parent Title (English): | Electronic Journal of Probability |
| Publisher: | Institute of Mathematical Statistics |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2021 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/06/27 |
| Volume: | 26 |
| First Page: | 1 |
| Last Page: | 38 |
| DOI: | https://doi.org/10.1214/21-ejp725 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
