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Journal of Statistical Physics

, Volume 84, Issue 3–4, pp 415–454 | Cite as

A Brownian motion version of the directed polymer problem

  • Joseph G. Conlon
  • Peder A. Olsen
Articles

Abstract

Consider a Brownian particle in three dimensions in a random environment. The environment is determined by a potential random in space and time. It is shown that at small noise the large-time behavior of the particle is diffusive. The diffusion constant depends on the environment. This work generalizes previous results for random walk in a random environment. In these results the diffusion constant does not depend on the environment.

Key Words

Directed polymer Brownian motion transfer matrix spectral gap 

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References

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Joseph G. Conlon
    • 1
  • Peder A. Olsen
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn Arbor

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