Basic properties of the Airy line ensemble

Duncan Dauvergne, Bálint Virág

Published 2018-12-02Version 1

The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper to make it more accessible to probabilists. The two main theorems are a representation in terms of independent Brownian bridges connecting a fine grid of points, and a modulus of continuity result for all lines. Along the way, we give tail bounds and moduli of continuity for nonintersecting ensembles, and a quick proof for the tightness for Dyson's Brownian motion converging to the Airy line ensemble.