Directed polymers on infinite graphs
Probability
2021-03-17 v1
Abstract
We study the directed polymer model for general graphs (beyond ) and random walks. We provide sufficient conditions for the existence or non-existence of a weak disorder phase, of an region, and of very strong disorder, in terms of properties of the graph and of the random walk. We study in some detail (biased) random walk on various trees including the Galton Watson trees, and provide a range of other examples that illustrate counter-examples to intuitive extensions of the /SRW result.
Cite
@article{arxiv.2010.09503,
title = {Directed polymers on infinite graphs},
author = {Clement Cosco and Inbar Seroussi and Ofer Zeitouni},
journal= {arXiv preprint arXiv:2010.09503},
year = {2021}
}