On self-repellent one dimensional random walks |
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Authors: | Erwin Bolthausen |
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Institution: | (1) Fachbereich Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, D-1000 Berlin 12, Germany;(2) Present address: Institut für Angewandte Mathematik der Universität, Rämistrasse 74, CH-8001 Zürich, Switzerland |
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Abstract: | Summary We consider an ordinary one dimensional recurrent random walk on. 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– for every self intersection of the path. 0<<1 is a parameter.It is shown that if the jump distribution of the random walk has an exponential moment and if is small enough then the displacement of the endpoint is asymptotically of the order of the length of the path.Partially supported by the Deutsche Forschungsgemeinschaft and the Akademie der Wissenschaften zu Berlin |
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