Fluctuations around the diagonal in Bernoulli-Exponential first passage percolation

Abstract

We prove that the rescaled one-point fluctuations of the boundary of the percolation cluster in the Bernoulli-Exponential first passage percolation around the diagonal converge to a new family of distributions. The limit law is indexed by the rescaled level of percolation $s\ge 0$, it is Gaussian for $s=0$ and it converges to the Tracy--Widom distribution as $s\to \infty$. For a fixed level $s>0$ the width of the cluster in the limit as a function of a time parameter $t$ is of order $t^{2/3}$ with Tracy--Widom fluctuations as in the discrete model.

14 pages, 1 figure

References in corpus (2)

• The Brownian web: Characterization and convergence
• Tracy-Widom asymptotics for a river delta model