Stationary cocycles and Busemann functions for the corner growth model

@article{Georgiou2015StationaryCA,
  title={Stationary cocycles and Busemann functions for the corner growth model},
  author={Nicos Georgiou and Firas Rassoul-Agha and Timo Sepp{\"a}l{\"a}inen},
  journal={Probability Theory and Related Fields},
  year={2015},
  volume={169},
  pages={177-222}
}
We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as boundary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where… 

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  • F. Rassoul-Agha
  • Mathematics
    Proceedings of Symposia in Applied Mathematics
  • 2018
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We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable

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We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable

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