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Title: Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps
Authors: Comets, Francis
Fukushima, Ryoki
Nakajima, Shuta
Yoshida, Nobuo
Author's alias: 福島, 竜輝
中島, 秀太
Keywords: Directed polymer
Random environment
First passage percolation
Zero temperature
Ground states
Issue Date: Nov-2015
Publisher: Springer US
Journal title: Journal of Statistical Physics
Volume: 161
Issue: 3
Start page: 577
End page: 597
Abstract: We study asymptotics of the free energy for the directed polymer in random environment. The polymer is allowed to make unbounded jumps and the environment is given by Bernoulli variables. We first establish the existence and continuity of the free energy including the negative infinity value of the coupling constant β . Our proof of existence at β=−∞ differs from existing ones in that it avoids the direct use of subadditivity. Secondly, we identify the asymptotics of the free energy at β=−∞ in the limit of the success probability of the Bernoulli variables tending to one. It is described by using the so-called time constant of a certain directed first passage percolation. Our proof relies on a certain continuity property of the time constant, which is of independent interest.
Rights: This is a post-peer-review, pre-copyedit version of an article published in 'Journal of Statistical Physics'. The final authenticated version is available online at:
The full-text file will be made open to the public on 09 August 2016 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
DOI(Published Version): 10.1007/s10955-015-1347-1
Appears in Collections:Journal Articles

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