Diffusion of directed polymers in a strong random environment

Peder Olsen, Renming Song

Research output: Contribution to journalArticlepeer-review


We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. It was shown by Imbrie and Spencer that in spatial dimensions three or above the behavior is diffusive if the directed polymer interacts weakly with the environment and if the random environment follows the Bernoulli distribution. Under the same assumption on the random environment as that of Imbrie and Spencer, we establish that in spatial dimensions four or above the behavior is still diffusive even when the directed polymer interacts strongly with the environment. More generally, we can prove that, if the random environment is bounded and if the supremum of the support of the distribution has a positive mass, then there is an integer d0 such that in dimensions higher than d0 the behavior of the random polymer is always diffusive.

Original languageEnglish (US)
Pages (from-to)727-738
Number of pages12
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - May 1996
Externally publishedYes


  • Directed polymers
  • Martingales
  • Random environment
  • Random walks

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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