Stationary half-space geometric last passage percolation

Abstract: We study stationary last passage percolation (LPP) with geometric weights in a half-space geometry. The two-parameter stationary measure for this model has recently been characterized, with the boundary parameter r and the parameter s which describes the initial condition at infinity. For each pair (r, s) in the high-density phase, we derive an explicit formula for the distribution of the stationary LPP along the diagonal and also find its asymptotic distribution under critical scaling.