Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps

• Comets, Francis

  Laboratoire Probabilités et Modélisation Aléatoire, Université Paris Diderot

• Fukushima, Ryoki

  Research Institute in Mathematical Sciences, Kyoto University

• Nakajima, Shuta

  Research Institute in Mathematical Sciences, Kyoto University

• Yoshida, Nobuo

  Graduate School of Mathematics, Nagoya University

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.

Journal

• Journal of Statistical Physics

  Journal of Statistical Physics 161 (3), 577-597, 2015-11

  Springer US

Keywords

• Directed polymer
• Random environment
• First passage percolation
• Zero temperature
• Ground states

Details

• CRID: 1050001202476442752
• NII Article ID: 120006644059
• ISSN: 00224715
• ISSN: 15729613
• DOI: 10.1007/s10955-015-1347-1
• HANDLE: 2433/241738
• Web Site: http://link.springer.com/content/pdf/10.1007/s10955-015-1347-1.pdf
• Web Site: http://link.springer.com/article/10.1007/s10955-015-1347-1/fulltext.html
• Web Site: http://link.springer.com/content/pdf/10.1007/s10955-015-1347-1
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN