A remark on diffusion of directed polymers in random environments

Renming Song, Xian Yin Zhou

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. Under minimal assumptions on the distribution of the environment, we prove that this system has diffusive behavior with probability one if d >2 and β < β0, where β0 is defined in terms of the probability that the symmetric nearest neighbor random walk on the d-dimensional integer lattice ever returns to its starting point. We also obtain a precise estimate for the mean square displacement of this system.

Original languageEnglish (US)
Pages (from-to)277-289
Number of pages13
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Oct 1996
Externally publishedYes


  • Directed polymers
  • Martingales
  • Random environment
  • Random walks

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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