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 Electronic Communications in Probability > Vol. 3 (1998) > Paper 5 open journal systems 

Loop-Erased Walks Intersect Infinitely Often in Four Dimensions

Gregory F. Lawler, Duke University

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

Published on: June 6, 1998

  1. A. Guttman and R. Bursill, Critical exponent for the loop-erased self-avoiding walk by Monte Carlo methods, J. Stat. Phys. 59 (1990), 1--9 Math Review article not available.
  2. G. Lawler, Intersections of Random Walks, Birkhauser-Boston (1991). Math Review link
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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.
  7. F. Spitzer, Principles of Random Walk, Springer-Verlag (1996).

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Electronic Communications in Probability. ISSN: 1083-589X