The invariant measure of PushASEP with a wall and point-to-line last passage percolation

TL;DR

This paper establishes a connection between the invariant measure of PushASEP with a wall and point-to-line last passage percolation times, revealing new insights into the system's long-term behavior and its relation to random walks.

Contribution

It demonstrates that the invariant measure of PushASEP with a wall matches the distribution of certain last passage percolation times, linking particle systems to percolation models.

Findings

Invariant measure equals distribution of point-to-line last passage percolation times.

Largest coordinates match the supremum of a non-colliding random walk.

Provides a new probabilistic representation for PushASEP with a wall.

Abstract

We consider an interacting particle system on the lattice involving pushing and blocking interactions, called PushASEP, in the presence of a wall at the origin. We show that the invariant measure of this system is equal in distribution to a vector of point-to-line last passage percolation times in a random geometrically distributed environment. The largest co-ordinates in both of these vectors are equal in distribution to the all-time supremum of a non-colliding random walk.