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.

Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point / Bisi E; Liao Y; Saenz A; Zygouras N. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 402:(2023), pp. 285-333. [10.1007/s00220-023-04723-8]

Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point

Bisi E;
2023

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.
2023
402
285
333
Bisi E; Liao Y; Saenz A; Zygouras N
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1386115
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