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Multi-point distribution of discrete time periodic TASEP
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Liao, Yuchen (2022) Multi-point distribution of discrete time periodic TASEP. Probability Theory and Related Fields, 182 . pp. 1053-1131. doi:10.1007/s00440-021-01107-8 ISSN 0178-8051.
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WRAP-Multi-point-distribution-discrete-time-periodic-TASEP-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (1030Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/s00440-021-01107-8
Abstract
We study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula is obtained for general initial conditions. The formula involves contour integrals of Fredholm determinants with kernels acting on certain discrete spaces. For a class of initial conditions satisfying certain technical assumptions, we are able to derive large-time, large-period limit of the joint distribution, under the relaxation time scale t=O(L3/2) when the height fluctuations are critically affected by the finite geometry. The assumptions are verified for the step and flat initial conditions. As a corollary we obtain the multi-point distribution of discrete time TASEP on the whole integer lattice Z by taking the period L large enough so that the finite-time distribution is not affected by the boundary. The large time limit for the multi-time distribution of discrete time TASEP on Z is then obtained for the step initial condition.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Stochastic processes , Statistical mechanics , Percolation (Statistical physics), Integrals , Discrete-time systems | ||||||||
| Journal or Publication Title: | Probability Theory and Related Fields | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0178-8051 | ||||||||
| Official Date: | April 2022 | ||||||||
| Dates: |
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| Volume: | 182 | ||||||||
| Page Range: | pp. 1053-1131 | ||||||||
| DOI: | 10.1007/s00440-021-01107-8 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 2 March 2022 | ||||||||
| Date of first compliant Open Access: | 2 March 2022 | ||||||||
| RIOXX Funder/Project Grant: |
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