Variational Formulas and Cocycle solutions for Directed Polymer and Percolation Models

@article{Georgiou2013VariationalFA,
  title={Variational Formulas and Cocycle solutions for Directed Polymer and Percolation Models},
  author={Nicos Georgiou and Firas Rassoul-Agha and Timo Sepp{\"a}l{\"a}inen},
  journal={Communications in Mathematical Physics},
  year={2013},
  volume={346},
  pages={741-779}
}
We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for models in arbitrary dimension, steps of the admissible paths can be general, the environment process is ergodic under spatial translations, and the potential accumulated along a path can depend on the environment and the next step of the… 
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