TY - JOUR
T1 - Intermediate Disorder Regime for Half-Space Directed Polymers
AU - Wu, Xuan
N1 - Funding Information:
The author is very grateful to Ivan Corwin for his incredible guidance and many encouraging conversations, and also extends thanks to Guillaume Barraquand and Promit Ghosal for their helpful discussions related to this work. The author is in particular very grateful to an anonymous referee for pointing out many typos/errors and for providing numerous suggestions. The author was partially supported by NSF grant of Ivan Corwin’s DMS-1664650 as well as the NSF grant DMS-1441467 for PCMI, at which this work started.
Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/12
Y1 - 2020/12
N2 - We consider the convergence of point-to-point partition functions for the half-space directed polymer model in dimension 1+1 in the intermediate disorder regime as introduced for the full space model by Alberts, Khanin and Quastel in [1]. By scaling the inverse temperature as βn- 1 / 4, the point-to-point partition function converges to the chaos series for the solution to stochastic heat equation with Robin boundary condition and delta initial data. Furthermore, the convergence result is then applied to the exact-solvable log-gamma directed polymer model in a half-space.
AB - We consider the convergence of point-to-point partition functions for the half-space directed polymer model in dimension 1+1 in the intermediate disorder regime as introduced for the full space model by Alberts, Khanin and Quastel in [1]. By scaling the inverse temperature as βn- 1 / 4, the point-to-point partition function converges to the chaos series for the solution to stochastic heat equation with Robin boundary condition and delta initial data. Furthermore, the convergence result is then applied to the exact-solvable log-gamma directed polymer model in a half-space.
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U2 - 10.1007/s10955-020-02668-z
DO - 10.1007/s10955-020-02668-z
M3 - Article
AN - SCOPUS:85096119578
SN - 0022-4715
VL - 181
SP - 2372
EP - 2403
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 6
ER -