Uniform convergence 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.

48 pages, 6 figures

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• Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
• Edge scaling limit of Dyson Brownian motion at equilibrium for general $\beta \ge 1$
• Infinite order phase transition in the slow bond TASEP
• The geometry of coalescing random walks, the Brownian web distance and KPZ universality
• Tightness of $(H,H^{RW})$-Gibbsian line ensembles