Directed Polymers on Infinite Graphs

Clément Cosco, Inbar Seroussi, Ofer Zeitouni*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the directed polymer model for general graphs (beyond Zd) and random walks. We provide sufficient conditions for the existence or non-existence of a weak disorder phase, of an L2 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 Zd/SRW result.

Original languageEnglish
Pages (from-to)395-432
Number of pages38
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Aug 2021
Externally publishedYes


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