The half-space Airy stat process

TL;DR

This paper investigates the multipoint distribution in stationary half-space last passage percolation with exponential weights, introducing the novel half-space Airy stat process as a generalization of the Airy stat, extending previous one-point results.

Contribution

The paper derives finite-size and asymptotic multipoint distribution results and introduces the half-space Airy stat process, a new one-parameter generalization of the Airy stat process.

Findings

Introduction of the half-space Airy stat process as a new universal limit.

Extension of one-point distribution results to multipoint cases.

Identification of the process as a generalization of the Airy stat far from the diagonal.

Abstract

We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new one-parameter process we call half-space Airy stat. It is a one-parameter generalization of the Airy stat process of Baik-Ferrari-P\'ech\'e, which is recovered far away from the diagonal. All these results extend the one-point results previously proven by the authors.