Ofer Busani

University of Bonn (Hausdorff Center for Mathematics)

Diffusive scaling limit for the Busemann process in last passage percolation

Probability Seminar

3rd December 2021, 3:30 pm – 4:30 pm
Fry Building, 2.04 (also on Zoom)

In last passage percolation, i.i.d. weights are assigned to the vertices of the lattice Z^2 and one is interested in the behaviour of geodesics - up-right paths on the lattice that maximize the weight collected between their endpoints. Of particular interests is the behaviour 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 behaviour of infinite geodesics. In this talk I will describe the scaling limit of the Busemann process in exponential last passage percolation, discuss the motivation behind it as well as some new ideas and connections from the proof.

Organisers: Benjamin Lees, Jessica Jay

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