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2008 Self-repelling random walk with directed edges on Z
Balint Veto, Balint Toth
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Electron. J. Probab. 13: 1909-1926 (2008). DOI: 10.1214/EJP.v13-570


We consider a variant of self-repelling random walk on the integer lattice Z where the self-repellence is defined in terms of the local time on oriented edges. The long-time asymptotic scaling of this walk is surprisingly different from the asymptotics of the similar process with self-repellence defined in terms of local time on unoriented edges. We prove limit theorems for the local time process and for the position of the random walker. The main ingredient is a Ray-Knight-type of approach. At the end of the paper, we also present some computer simulations which show the strange scaling behaviour of the walk considered.


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Balint Veto. Balint Toth. "Self-repelling random walk with directed edges on Z." Electron. J. Probab. 13 1909 - 1926, 2008.


Accepted: 30 October 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60036
MathSciNet: MR2453550
Digital Object Identifier: 10.1214/EJP.v13-570

Primary: 60G50
Secondary: 82B41 , 82C41

Keywords: coupling , Local time , one dimension , oriented edges , random walks with long memory , Ray-Knight-theory , self-repelling


Vol.13 • 2008
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