TY - JOUR
T1 - Directed Polymers on Infinite Graphs
AU - Cosco, Clément
AU - Seroussi, Inbar
AU - Zeitouni, Ofer
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
PY - 2021/8
Y1 - 2021/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85101822312&partnerID=8YFLogxK
U2 - 10.1007/s00220-021-04034-w
DO - 10.1007/s00220-021-04034-w
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AN - SCOPUS:85101822312
SN - 0010-3616
VL - 386
SP - 395
EP - 432
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -