We consider an ordinary one-dimensional recurrent random walk on ℤ. A self-repellent random walk is defined by changing the ordinary law of the random walk in the following way: A path gets a new relative weight by multiplying the old one with a factor 1-β for every self intersection of the path. 0<β<1 is a parameter.

It is shown that if the jump distribution of the random walk has an exponential moment and if β is small enough then the displacement of the endpoint is asymptotically of the order of the length of the path.

Bolthausen, E (1990). *On self-repellent one-dimensional random walks.* Probability Theory and Related Fields, 86(4):423-441.

## Abstract

We consider an ordinary one-dimensional recurrent random walk on ℤ. A self-repellent random walk is defined by changing the ordinary law of the random walk in the following way: A path gets a new relative weight by multiplying the old one with a factor 1-β for every self intersection of the path. 0<β<1 is a parameter.

It is shown that if the jump distribution of the random walk has an exponential moment and if β is small enough then the displacement of the endpoint is asymptotically of the order of the length of the path.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | self-repellent random walk; exponential moment |

Language: | English |

Date: | 1990 |

Deposited On: | 21 May 2010 08:08 |

Last Modified: | 05 Apr 2016 13:29 |

Publisher: | Springer |

ISSN: | 0178-8051 |

Additional Information: | The original publication is available at www.springerlink.com |

Publisher DOI: | https://doi.org/10.1007/BF01198167 |

Related URLs: | http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0691.60060 |

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