Free Energy of the Cauchy Directed Polymer Model at High Temperature

Ran Wei*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1057-1085
Number of pages29
JournalJournal of Statistical Physics
Issue number4
Publication statusPublished - 1 Aug 2018
Externally publishedYes


  • Cauchy directed polymer
  • Free energy
  • Very strong Disorder


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