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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


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.


Full text: PDF

Pages: 35-42

Published on: June 6, 1998
Bibliography
  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
  3. G. Lawler, Escape probabilities for slowly recurrent sets, Probab. Theory Relat. Fields 94, 91--117 (1992). Math Review link
  4. G. Lawler, Cut points for simple random walk, Electronic J. of Prob. 1, #13 (1996). Math Review link
  5. G. Lawler, Strict concavity of the intersection exponent for Brownian motion in two and three dimensions, preprint (1997). Math Review article not available.
  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