• Corpus ID: 180260668

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

@inproceedings{Janjigian2019BUSEMANNFA,
  title={BUSEMANN FUNCTIONS AND GIBBS MEASURES IN DIRECTED POLYMER MODELS ON Z2 BY CHRISTOPHER JANJIGIAN*},
  author={Christopher Janjigian and Firas Rassoul-Agha},
  year={2019}
}
We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices. We construct covariant cocycles and use them to prove new results on existence, uniqueness/nonuniqueness, and asymptotic directions of semi-infinite polymer measures (solutions to the Dobrushin–Lanford–Ruelle equations). We also prove nonexistence of covariant or deterministically directed… 

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