<div class="csl-bib-body">
<div class="csl-entry">Bisi, E., Liao, Y., Saenz, A., & Zygouras, N. (2023). Non-intersecting Path Constructions for TASEP with Inhomogeneous Rates and the KPZ Fixed Point. <i>Communications in Mathematical Physics</i>, <i>402</i>, 285–333. https://doi.org/10.1007/s00220-023-04723-8</div>
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dc.identifier.issn
0010-3616
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191221
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dc.description.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.
en
dc.language.iso
en
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dc.publisher
SPRINGER
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dc.relation.ispartof
Communications in Mathematical Physics
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
TASEP
en
dc.subject
Non-intersecting paths
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dc.subject
KPZ fixed point
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dc.subject
RSK correspondence
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dc.title
Non-intersecting Path Constructions for TASEP with Inhomogeneous Rates and the KPZ Fixed Point