TY - JOUR
T1 - Weak Coupling Limits for Directed Polymers in Tube Environments
AU - Wei, Ran
AU - Yu, Jinjiong
N1 - Funding Information:
Ran Wei is supported by a public grant overseen by the French National Research Agency, ANR SWiWS (ANR-17-CE40-0032-02). Jinjiong Yu is supported by NSFC 12101238. We would like to thank Rongfeng Sun and Quentin Berger for helpful suggestions and discussions. We also thank Francesco Caravenna and Nikos Zygouras for telling us some references. Finally, we thank the anonymous referees, who help us greatly improve the quality of the paper and correct some mistakes.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/3
Y1 - 2022/3
N2 - In this paper, we study a model of directed polymers in random environment, where the environment is restricted to a time-space tube whose spatial width grows polynomially with time. It can be viewed as an interpolation between the disordered pinning model and the classic directed polymer model. We prove weak coupling limits for the directed polymer partition functions in such tube environments in all dimensions, as the inverse temperature vanishes at a suitable rate. As the tube width varies, transitions between regimes of disorder irrelevance, marginal relevance and disorder relevance are observed.
AB - In this paper, we study a model of directed polymers in random environment, where the environment is restricted to a time-space tube whose spatial width grows polynomially with time. It can be viewed as an interpolation between the disordered pinning model and the classic directed polymer model. We prove weak coupling limits for the directed polymer partition functions in such tube environments in all dimensions, as the inverse temperature vanishes at a suitable rate. As the tube width varies, transitions between regimes of disorder irrelevance, marginal relevance and disorder relevance are observed.
KW - Directed polymer in tube environments
KW - Disorder relevance
KW - Marginal relevance
KW - Weak coupling limit
UR - http://www.scopus.com/inward/record.url?scp=85124726837&partnerID=8YFLogxK
U2 - 10.1007/s10955-022-02887-6
DO - 10.1007/s10955-022-02887-6
M3 - Article
AN - SCOPUS:85124726837
SN - 0022-4715
VL - 186
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 3
M1 - 43
ER -