Open Access
2021 The invariant measure of PushASEP with a wall and point-to-line last passage percolation
Will FitzGerald
Author Affiliations +
Electron. J. Probab. 26: 1-26 (2021). DOI: 10.1214/21-EJP661


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.

Funding Statement

I am grateful for the financial support of the Royal Society Enhancement Award ‘Log-correlated Gaussian fields and symmetry classes in random matrix theory RGF\EA\181085.’


I am very grateful to Jon Warren for helpful and stimulating discussions and to Neil O’Connell for suggesting the approach in Section 2.1.


Download Citation

Will FitzGerald. "The invariant measure of PushASEP with a wall and point-to-line last passage percolation." Electron. J. Probab. 26 1 - 26, 2021.


Received: 29 October 2020; Accepted: 7 June 2021; Published: 2021
First available in Project Euclid: 23 June 2021

Digital Object Identifier: 10.1214/21-EJP661

Primary: 60C05 , 60J45 , 60K35

Keywords: interacting particle systems , non-colliding random walks , point-to-line last passage percolation , symplectic Schur functions

Vol.26 • 2021
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