Kostya Khanin

[Balint Virag]

Dear All,

We have a seminar on Monday, Feb 10, 3:10pm, Fields 210.

Konstantin Khanin, UofT

First Passage Percolation in a Product-Type Random Environment

The talk is based on a joint work with Yuri Bakhtin, András Mészáros and
Jeremy Voltz.

We consider a first passage percolation model in dimension 1 + 1 with
potential given by the product of a spatial i.i.d. potential with
symmetric bounded distribution and an independent i.i.d. in time
sequence of signs. We assume that the density of the spatial potential
near the edge of its support behaves as a power, with exponent κ > −1.
We investigate the linear growth rate of the actions of optimal
point-to-point lazy random walk paths as a function of the path slope
and describe the structure of the resulting shape function. It has a
corner at 0 and, although its restriction to positive slopes cannot be
linear, we prove that it has a flat edge near 0 if κ > 0. For optimal
point-to-line paths, we study their actions and locations of favorable
edges that the paths tend to reach and stay at. Under an additional
assumption on the time it takes for the optimal path to reach the
favorable location, we prove that appropriately normalized actions
converge to a limiting distribution that can be viewed as a counterpart
of the Tracy–Widom law. Since the scaling exponent and the limiting
distribution depend only on the parameter κ, our results provide a
description of a new universality class.