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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 62 open journal systems 


Self-repelling random walk with directed edges on Z

Balint Veto, Budapest University of Technology
Balint Toth, Budapest University of Technology


Abstract
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.


Full text: PDF

Pages: 1909-1926

Published on: October 30, 2008


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Electronic Journal of Probability. ISSN: 1083-6489