### Geometry of the corner growth model

Probability Seminar

31st May 2019, 3:30 pm – 4:30 pm

Main Maths Building, SM4

The corner growth model is a last-passage percolation model of random growth on the square

lattice. It lies at the nexus of several branches of mathematics: probability, statistical

physics, queueing theory, combinatorics, and integrable systems. It has been studied

intensely for 40 years. We review properties of the geodesics, Busemann functions and

competition interfaces of the corner growth model and present new qualitative and

quantitative results on the overall geodesic picture and the joint distributions of the

Busemann functions. Based on collaborations with Louis Fan (Indiana), Firas Rassoul-Agha

and Chris Janjigian (Utah).

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