Airy wanderer line ensembles

TL;DR

This paper constructs new determinantal point processes and line ensembles generalizing previous Airy kernel models, demonstrating their properties and connections to Brownian Gibbs measures.

Contribution

It introduces a broad class of generalized Airy line ensembles with the Brownian Gibbs property, extending earlier wanderer ensembles.

Findings

Constructed determinantal point processes for generalized Airy kernels.

Established the Brownian Gibbs property for a subset of these ensembles.

Generalized wanderer line ensembles beyond previous models.

Abstract

In (J. Stat. Phys. 132, 275-290, 2008) Borodin and P\'ech\'e introduced a generalization of the extended Airy kernel based on two infinite sets of parameters. For an arbitrary choice of parameters we construct determinantal point processes on $\mathbb{R}^2$ for these generalized kernels. In addition, for a subset of the parameter space we show that the point processes can be lifted to line ensembles on $\mathbb{R}$, which satisfy the Brownian Gibbs property. Our ensembles generalize the wanderer line ensembles introduced by Corwin and Hammond in (Invent. Math. 195, 441-508, 2014).