Bolthausen, E (1990). On self-repellent one-dimensional random walks. Probability Theory and Related Fields, 86(4):423-441.
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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.
|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|
|Deposited On:||21 May 2010 08:08|
|Last Modified:||05 Apr 2016 13:29|
|Additional Information:||The original publication is available at www.springerlink.com|
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