We consider random walks whose laws are perturbed in an irregular way by a second random mechanism, the so-called random environment. The perturbation acts in such a way that visits to certain randomly chosen points are favoured or disfavoured. Several models have been proposed in the mathematical physics literature, sharing the common feature that only very few facts are known at a rigorous mathematical level. We present here some of these models and some problems connected with them.

Bolthausen, E (1991). *On directed polymers in a random environment.* In: Basawa, I V; Taylor, R L. Selected Proceedings of the Sheffield Symposium on Applied Probability (Sheffield, 1989). Hayward, CA: Institute of Mathematical Statistics, 41-47.

## Abstract

We consider random walks whose laws are perturbed in an irregular way by a second random mechanism, the so-called random environment. The perturbation acts in such a way that visits to certain randomly chosen points are favoured or disfavoured. Several models have been proposed in the mathematical physics literature, sharing the common feature that only very few facts are known at a rigorous mathematical level. We present here some of these models and some problems connected with them.

## Citations

## Additional indexing

Item Type: | Book Section, refereed, original work |
---|---|

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | directed polymer; exponential martingale; large deviations; likelihood ratio; random walk; statistical physics |

Language: | English |

Date: | 1991 |

Deposited On: | 20 May 2010 15:55 |

Last Modified: | 05 Apr 2016 13:28 |

Publisher: | Institute of Mathematical Statistics |

Series Name: | IMS Lecture Notes - Monograph Series |

Number: | 18 |

ISSN: | 0749-2170 |

ISBN: | 0-940600-25-0 |

Related URLs: | http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0773.60067 |

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