Summary
We consider an ordinary one dimensional recurrent random walk onℤ. 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−λ for every self intersection of the path. 0<λ<1 is a parameter.
It is shown that if the jump distribution of the random walk has an exponential moment and if λ is small enough then the displacement of the endpoint is asymptotically of the order of the length of the path.
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Partially supported by the Deutsche Forschungsgemeinschaft and the Akademie der Wissenschaften zu Berlin
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Bolthausen, E. On self-repellent one dimensional random walks. Probab. Th. Rel. Fields 86, 423–441 (1990). https://doi.org/10.1007/BF01198167
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DOI: https://doi.org/10.1007/BF01198167
Keywords
- Endpoint
- Stochastic Process
- Random Walk
- Probability Theory
- Mathematical Biology