Journal of Statistical Physics

, Volume 85, Issue 1–2, pp 277–289 | Cite as

A remark on diffusion of directed polymers in random environments

  • Renming Song
  • Xian Yin Zhou
Short Communications


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 ifd>2 and β<β0, where β0 is defined in terms of the probability that the symmetric nearest neighbor random walk on thed-dimensional integer lattice ever returns to its starting point. We also obtain a precise estimate for the mean square displacement of this system.

Key Words

Random walks directed polymers random environment martingales 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Renming Song
    • 1
  • Xian Yin Zhou
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of MichiganAnn Arbor
  2. 2.Institut für MathematikRuhr-Universität BochumBochumGermany
  3. 3.Department of MathematicsBeijing Normal UniversityBeijingChina

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