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Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point
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Bisi, Elia, Liao, Yuchen, Saenz, Axel and Zygouras, Nikos (2023) Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point. Communications in Mathematical Physics, 402 (1). pp. 285-333. doi:10.1007/s00220-023-04723-8 ISSN 0010-3616.
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WRAP-non-intersecting-path-constructions-TASEP-inhomogeneous-rates-KPZ-fixed-point-Zygouras-2023.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (865Kb) | Preview |
Official URL: https://doi.org/10.1007/s00220-023-04723-8
Abstract
We consider a discrete-time TASEP, where each particle jumps according to Bernoulli random variables with particle-dependent and time-inhomogeneous parameters. We use the combinatorics of the Robinson–Schensted–Knuth correspondence and certain intertwining relations to express the transition kernel of this interacting particle system in terms of ensembles of weighted, non-intersecting lattice paths and, consequently, as a marginal of a determinantal point process. We next express the joint distribution of the particle positions as a Fredholm determinant, whose correlation kernel is given in terms of a boundary-value problem for a discrete heat equation. The solution to such a problem finally leads us to a representation of the correlation kernel in terms of random walk hitting probabilities, generalizing the formulation of Matetski et al. (Acta Math. 227(1):115–203, 2021) to the case of both particle- and time-inhomogeneous rates. The solution to the boundary value problem in the fully inhomogeneous case appears with a finer structure than in the homogeneous case.
| 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 | ||||||||||||
| SWORD Depositor: | Library Publications Router | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Probabilities , Stochastic systems , Combinatorial analysis , Fredholm equations, Discrete-time systems , Mathematical Physics | ||||||||||||
| Journal or Publication Title: | Communications in Mathematical Physics | ||||||||||||
| Publisher: | Springer | ||||||||||||
| ISSN: | 0010-3616 | ||||||||||||
| Official Date: | August 2023 | ||||||||||||
| Dates: |
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| Volume: | 402 | ||||||||||||
| Number: | 1 | ||||||||||||
| Page Range: | pp. 285-333 | ||||||||||||
| DOI: | 10.1007/s00220-023-04723-8 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Date of first compliant deposit: | 27 July 2023 | ||||||||||||
| Date of first compliant Open Access: | 28 July 2023 | ||||||||||||
| RIOXX Funder/Project Grant: |
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