Directed Polymers on Infinite Graphs

Clément Cosco; Inbar Seroussi; Ofer Zeitouni

doi:10.1007/s00220-021-04034-w

Directed Polymers on Infinite Graphs

Clément Cosco, Inbar Seroussi, Ofer Zeitouni

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We study the directed polymer model for general graphs (beyond Z^d) 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 Z^d/SRW result.

Original language	English
Pages (from-to)	395-432
Number of pages	38
Journal	Communications in Mathematical Physics
Volume	386
Issue number	1
Early online date	1 Mar 2021
DOIs	https://doi.org/10.1007/s00220-021-04034-w
State	Published - Aug 2021

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s00220-021-04034-w

http://arxiv.org/abs/2010.09503License: Unspecified

Cite this

@article{b11cab5f9a6c4242bc9f31e23b33288c,

title = "Directed Polymers on Infinite Graphs",

abstract = "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.",

author = "Cl{\'e}ment Cosco and Inbar Seroussi and Ofer Zeitouni",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.",

year = "2021",

month = aug,

doi = "10.1007/s00220-021-04034-w",

language = "الإنجليزيّة",

volume = "386",

pages = "395--432",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Directed Polymers on Infinite Graphs

AU - Cosco, Clément

AU - Seroussi, Inbar

AU - Zeitouni, Ofer

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

M3 - مقالة

SN - 0010-3616

VL - 386

SP - 395

EP - 432

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -

Directed Polymers on Infinite Graphs

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this