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

Will FitzGerald

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arXiv · 2010.09011

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

Will FitzGerald

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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.

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Will FitzGerald. 2020-10-18. The invariant measure of PushASEP with a wall and point-to-line last passage percolation. https://arxiv.org/abs/2010.09011

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