## Abstract

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 d_{0} such that in dimensions higher than d_{0} the behavior of the random polymer is always diffusive.

Original language | English (US) |
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Pages (from-to) | 727-738 |

Number of pages | 12 |

Journal | Journal of Statistical Physics |

Volume | 83 |

Issue number | 3-4 |

DOIs | |

State | Published - May 1996 |

Externally published | Yes |

## Keywords

- Directed polymers
- Martingales
- Random environment
- Random walks

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics