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Petrov, Leonid and Saenz, Axel (2022) Mapping TASEP back in time. Probability Theory and Related Fields, 182 . pp. 481-530. doi:10.1007/s00440-021-01074-0 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-021-01074-0
Abstract
We obtain a new relation between the distributions μt at different times t≥0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions μt backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving μt which in turn brings new identities for expectations with respect to μt. The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Probabilities, Markov processes | ||||||||||
| Journal or Publication Title: | Probability Theory and Related Fields | ||||||||||
| Publisher: | Springer | ||||||||||
| ISSN: | 0178-8051 | ||||||||||
| Official Date: | February 2022 | ||||||||||
| Dates: |
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| Volume: | 182 | ||||||||||
| Page Range: | pp. 481-530 | ||||||||||
| DOI: | 10.1007/s00440-021-01074-0 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||
| Date of first compliant deposit: | 8 August 2022 | ||||||||||
| Date of first compliant Open Access: | 10 August 2022 | ||||||||||
| RIOXX Funder/Project Grant: |
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