Loop-Erased Walks Intersect Infinitely Often in Four Dimensions

Gregory F. Lawler (Duke University)

Abstract


In this short note we show that the paths two independent loop-erased random walks in four dimensions intersect infinitely often. We actually prove the stronger result that the cut-points of the two walks intersect infinitely often.

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Pages: 35-42

Publication Date: June 6, 1998

DOI: 10.1214/ECP.v3-991

References

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  6. R. Lyons, Y. Peres, and O. Schramm, Can a Markov chain intersect an independent copy only in its loops, to appear. Math Review article not available.
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