Universality of geodesic tree in last passage percolation

Abstract: In Last Passage Percolation (LPP) one assumes i.i.d. weights on the lattice Z^2. The geodesic from the anti-diagonal h(x)=-x to the point (N,N) is an up-right path starting from h and terminating at (N,N) on which the total weight is maximal. Consider now a cylinder H of width εN^2/3 and length ε^{3/2-}N centered around the point (N,N) and along the straight line going from the point (0,0) to the point (N,N). The geodesic tree consists of all the geodesics going from h and terminating in the cylinder H. We show that for exponential LPP, for a large class of weights on h(x) and with high probability, the geodesic tree coincides on H with a universal stationary tree.

mathematical physicscombinatoricsprobabilityrepresentation theorystatistics theory

Audience: researchers in the topic

Junior Integrable Probability Seminar

Series comments: The Junior Integrable Probability Seminar is a series of talks taking place online and involving young researchers working in Integrable Probability and related fields. Go to sites.google.com/view/junior-ips for zoom link and password for the talk a day before the seminar.