Geometry of geodesics through Busemann measures in directed last-passage percolation

@article{Janjigian2022GeometryOG,
  title={Geometry of geodesics through Busemann measures in directed last-passage percolation},
  author={Christopher Janjigian and Firas Rassoul-Agha and Timo Seppalainen},
  journal={Journal of the European Mathematical Society},
  year={2022}
}
We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The structure of the geodesics is studied through the properties of the Busemann functions viewed as a stochastic process indexed by the asymptotic direction. In the exactly solvable exponential model, we give the first complete characterization of the uniqueness and… 

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