Open Access
2020 PushTASEP in inhomogeneous space
Leonid Petrov
Electron. J. Probab. 25: 1-25 (2020). DOI: 10.1214/20-EJP517


We consider the PushTASEP (pushing totally asymmetric simple exclusion process, also sometimes called long-range TASEP) with the step initial configuration evolving in an inhomogeneous space. That is, the rate of each particle’s jump depends on the location of this particle. We match the distribution of the height function of this PushTASEP with Schur processes. Using this matching and determinantal structure of Schur processes, we obtain limit shape and fluctuation results which are typical for stochastic particle systems in the Kardar-Parisi-Zhang universality class. PushTASEP is a close relative of the usual TASEP. In inhomogeneous space the former is integrable, while the integrability of the latter is not known.


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Leonid Petrov. "PushTASEP in inhomogeneous space." Electron. J. Probab. 25 1 - 25, 2020.


Received: 21 October 2019; Accepted: 26 August 2020; Published: 2020
First available in Project Euclid: 21 September 2020

zbMATH: 07252708
MathSciNet: MR4161124
Digital Object Identifier: 10.1214/20-EJP517

Primary: 82C22
Secondary: 60C05

Keywords: limit shape , PushTASEP , Schur process , Tracy-Widom distribution

Vol.25 • 2020
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