Multiple-transit paths and density correlation functions in PASEP

TL;DR

This paper explores the PASEP model's steady-state properties by mapping it to a walk model, revealing how multiple transits relate to density correlations and contacts with the horizontal axis.

Contribution

It introduces a novel mapping of PASEP with shocks to an equilibrium walk model, linking multiple-point density correlations to path contacts.

Findings

Density correlation functions relate to path contacts with the axis.

Multiple transits in the walk model correspond to shock structures in PASEP.

The approach provides a new perspective on PASEP steady states.

Abstract

We consider the partially asymmetric simple exclusion process (PASEP) when its steady-state probability distribution function can be written in terms of a linear superposition of product measures with a finite number of shocks. In this case the PASEP can be mapped into an equilibrium walk model, defined on a diagonally rotated square lattice, in which each path of the walk model has several transits with the horizontal axis. We particularly show that the multiple-point density correlation function in the PASEP is related to the probability that a path has multiple contacts with the horizontal axis from the above or below.