Estimates of Random Walk Exit Probabilities and Application to Loop-Erased Random Walk
نویسندگان
چکیده
منابع مشابه
Scaling Limit of Loop-erased Random Walk
The loop-erased random walk (LERW) was first studied in 1980 by Lawler as an attempt to analyze self-avoiding walk (SAW) which provides a model for the growth of a linear polymer in a good solvent. The self-avoiding walk is simply a path on a lattice that does not visit the same site more than once. Proving things about the collection of all such paths is a formidable challenge to rigorous math...
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Lawler, Schramm and Werner showed that the scaling limit of the loop-erased random walk on Z2 is SLE2. We consider scaling limits of the loop-erasure of random walks on other planar graphs (graphs embedded into C so that edges do not cross one another). We show that if the scaling limit of the random walk is planar Brownian motion, then the scaling limit of its loop-erasure is SLE2. Our main co...
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We give an alternative proof of the existence of the scaling limit of loop-erased random walk which does not use Löwner’s differential equation.
متن کاملConvergence of loop-erased random walk in the natural parameterization
We prove that loop-erased random walk parametrized by renormalized length converges in the lattice size scaling limit to SLE2 parametrized by Minkowski content.
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2005
ISSN: 1083-6489
DOI: 10.1214/ejp.v10-294