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.
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