# 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…

## 57 Citations

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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…

### BUSEMANN FUNCTIONS AND GIBBS MEASURES IN DIRECTED POLYMER MODELS ON Z2 BY CHRISTOPHER JANJIGIAN*

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### Coalescence estimates for the corner growth model with exponential weights

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These lecture notes discuss several related features of the exactly solvable two-dimensional corner growth model with exponentially distributed weights. A key property of this model is the…

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