TY - JOUR
T1 - Free Energy of the Cauchy Directed Polymer Model at High Temperature
AU - Wei, Ran
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - We study the Cauchy directed polymer model on Z1 + 1, where the underlying random walk is in the domain of attraction to the 1-stable law. We show that, if the random walk satisfies certain regularity assumptions and its symmetrized version is recurrent, then the free energy is strictly negative at any inverse temperature β> 0. Moreover, under additional regularity assumptions on the random walk, we can identify the sharp asymptotics of the free energy in the high temperature limit, namely, limβ→0β2log(-p(β))=-c.
AB - We study the Cauchy directed polymer model on Z1 + 1, where the underlying random walk is in the domain of attraction to the 1-stable law. We show that, if the random walk satisfies certain regularity assumptions and its symmetrized version is recurrent, then the free energy is strictly negative at any inverse temperature β> 0. Moreover, under additional regularity assumptions on the random walk, we can identify the sharp asymptotics of the free energy in the high temperature limit, namely, limβ→0β2log(-p(β))=-c.
KW - Cauchy directed polymer
KW - Free energy
KW - Very strong Disorder
UR - http://www.scopus.com/inward/record.url?scp=85048763986&partnerID=8YFLogxK
U2 - 10.1007/s10955-018-2086-x
DO - 10.1007/s10955-018-2086-x
M3 - Article
AN - SCOPUS:85048763986
SN - 0022-4715
VL - 172
SP - 1057
EP - 1085
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 4
ER -