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.
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.
"The invariant measure of PushASEP with a wall and point-to-line last passage percolation." Electron. J. Probab. 26 1 - 26, 2021. https://doi.org/10.1214/21-EJP661