Last-Passage Percolation Geometry Under Large Deviations
Organizer
Speaker
Lingfu Zhang
Time
Wednesday, June 11, 2025 2:45 PM - 4:15 PM
Venue
A3-2-303
Online
Zoom 435 529 7909
(BIMSA)
Abstract
In the KPZ universality class, a central family of models is two-dimensional last-passage percolation (LPP). In LPP, one considers a 2D i.i.d. random field (such as a collection of i.i.d. random variables indexed by $\mathbb{Z}^2$) and studies the geodesic connecting two points, i.e., the directed path that maximizes the sum (or integral) of the random field along it. A hallmark of KPZ behavior is the $2/3$ exponent for geodesic fluctuations, which has been established in exactly solvable models. A topic of recent interest is its large deviations, where the geodesic length is atypically large or small. Previous works have shown that the fluctuation exponent changes to $1/2$ (more localized) and $1$ (delocalized), respectively. In this talk, I will discuss more refined geometric pictures. Specifically, in a joint work with Ganguly and Hegde, we show that when the geodesic length is atypically large, the geodesic converges to a Brownian bridge. I will also describe a work in progress with Eriksson, Ganguly, and Prause, in which we show that the geodesic becomes “rigid” when its length is atypically small.