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Ofer Busani: Diffusive scaling limit for the Busemann process in last passage percolation

Time: Tue 2022-02-08 14.45 - 15.45

Location: Zoom, meeting ID: 698 3346 0369

Lecturer: Ofer Busani (University of Bonn)

Abstract

In last passage percolation, i.i.d. weights are assigned to the vertices of the lattice \(\mathbb{Z}^2\) and one is interested in the behavior of geodesics — up-right paths on the lattice that maximize the weight collected between their endpoints. Of particular interest is the behavior of infinite geodesics — infinite up-right paths such that any connected subset of them is a geodesic. One of the most useful tools in studying infinite geodesics is the Busemann process, a stochastic process that holds much information on the behavior of infinite geodesics. In this talk I will describe the scaling limit of the Busemann process in exponential last passage percolation, the motivation behind it, and discuss some new ideas and connections from the proof.