### 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.

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