Uniform convergence to the Airy line ensemble

TL;DR

This paper proves that certain classical integrable models of last passage percolation and nonintersecting random walks converge uniformly to the Airy line ensemble, using coupling and convergence techniques.

Contribution

It establishes uniform convergence of integrable models to the Airy line ensemble in all feasible directions, extending previous results through coupling methods.

Findings

Convergence of nonintersecting Bernoulli random walks in all directions.

Extension of convergence results to various models via coupling.

Uniform convergence on compact sets to the Airy line ensemble.

Abstract

We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our core approach is to show convergence of nonintersecting Bernoulli random walks in all feasible directions in the parameter space. We then use coupling arguments to extend convergence to other models.