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On self-repellent one-dimensional random walks


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.

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
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:06 Dec 2017 21:13
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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