Uniform convergence to the Airy line ensemble

Duncan Dauvergne, Mihai Nica, Bálint Virág

Published 2019-07-23Version 1

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.