PushTASEP in inhomogeneous space

TL;DR

This paper studies the PushTASEP in an inhomogeneous environment, revealing its integrability and connection to Schur processes, and derives limit shape and fluctuation results within the KPZ universality class.

Contribution

It establishes the integrability of inhomogeneous PushTASEP and links it to Schur processes, enabling analysis of limit shapes and fluctuations.

Findings

Matching of height function distribution with Schur processes

Derivation of limit shape in inhomogeneous PushTASEP

Fluctuation results consistent with KPZ universality

Abstract

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.