Structural properties of the Airy wanderer line ensembles

TL;DR

This paper studies the structural properties of Airy wanderer line ensembles, which are infinite-parameter generalizations of the Airy line ensemble arising in the KPZ universality class, revealing their continuous dependence on parameters and extremal nature.

Contribution

It establishes the continuous dependence of these ensembles on parameters, their monotone couplings, and their status as extreme points in the space of Brownian Gibbsian line ensembles.

Findings

Laws depend continuously on parameters.

Existence of multiple monotone couplings.

Ensembles are extreme points in their space.

Abstract

The Airy wanderer line ensembles are infinite-parameter generalizations of the classical Airy line ensemble that arise naturally as scaling limits of inhomogeneous (spiked) models in the Kardar-Parisi-Zhang universality class. In this paper, we establish several structural properties of these ensembles. Our results show their laws depend continuously on the parameters, which encode the asymptotic slopes of the ensemble's curves near positive and negative infinity. We further prove that these ensembles admit multiple monotone couplings with respect to their parameters. Finally, we show that the Airy wanderer line ensembles are extreme points in the space of all Brownian Gibbsian line ensembles on the real line.