Localization and Perron--Frobenius theory for directed polymers

@article{Bakhtin2009LocalizationAP,
  title={Localization and Perron--Frobenius theory for directed polymers},
  author={Yuri Bakhtin and Konstantin Khanin},
  journal={arXiv: Probability},
  year={2009}
}
We consider directed polymers in a random potential given by a deterministic profile with a strong maximum at the origin taken with random sign at each integer time. We study two main objects based on paths in this random potential. First, we use the random potential and averaging over paths to define a parabolic model via a random Feynman--Kac evolution operator. We show that for the resulting cocycle, there is a unique positive cocycle eigenfunction serving as a forward and pullback… 
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