Airy kernel with two sets of parameters in directed percolation and random matrix theory

TL;DR

This paper introduces a generalized Airy kernel with two parameter sets, which appears in the edge scaling limits of correlation kernels in directed percolation models and random matrix ensembles.

Contribution

The paper presents a new two-parameter extension of the Airy kernel and demonstrates its relevance in directed percolation and random matrix theory.

Findings

The generalized Airy kernel arises in the edge scaling limit of certain determinantal processes.

It connects directed percolation models with random matrix ensembles.

The kernel's parameters allow for a broader class of edge behaviors.

Abstract

We introduce a generalization of the extended Airy kernel with two sets of real parameters. We show that this kernel arises in the edge scaling limit of correlation kernels of determinantal processes related to a directed percolation model and to an ensemble of random matrices.