Stationary half-space geometric last passage percolation

TL;DR

This paper derives exact formulas and asymptotic limits for the stationary half-space geometric last passage percolation model, contributing to understanding the KPZ universality class in half-space geometries.

Contribution

It provides the first exact formulas for LPP values along the diagonal in the stationary half-space geometric model and analyzes their critical scaling limits.

Findings

Exact formulas for LPP along the diagonal across the phase diagram

Asymptotic limits under critical scaling for the model

Insights into the half-space KPZ fixed point with stationary initial conditions

Abstract

We consider the half-space geometric Last Passage Percolation model starting with stationary measures. We obtain exact formulas for LPP value along the diagonal $(N,N)$ across the entire phase diagram. We also obtain the limits of these distributions under critical scaling which should yield the one-point distribution of the half-space KPZ fixed point starting from stationary initial conditions.