Half-space Airy line ensembles

TL;DR

This paper introduces a new family of half-space Airy line ensembles that interpolate between avoiding Brownian bridges and reverse Brownian motions with alternating drifts, revealing their Pfaffian structure.

Contribution

It constructs a novel one-parameter family of half-space Airy line ensembles with explicit local descriptions and Pfaffian point process properties.

Findings

Ensembles are locally described by avoiding Brownian bridges away from the origin.

Near the origin, ensembles are described by avoiding reverse Brownian motions with alternating drifts.

Restrictions to finitely many lines form Pfaffian point processes with known crossover kernels.

Abstract

We construct a one-parameter family of infinite line ensembles on $[0, \infty)$ that are natural half-space analogues of the Airy line ensemble. Away from the origin these ensembles are locally described by avoiding Brownian bridges, and near the origin they are described by a sequence of avoiding reverse Brownian motions with alternating drifts, that depend on the parameter of the model. In addition, the restrictions of our ensembles to finitely many vertical lines form Pfaffian point processes with the crossover kernels obtained by Baik-Barraquand-Corwin-Suidan (Ann. Probab., 46(6), 3015-3089, 2018)