Loop-Erased Random Walk
نویسنده
چکیده
منابع مشابه
ar X iv : m at h / 06 11 77 5 v 1 [ m at h . PR ] 2 5 N ov 2 00 6 Colored loop - erased random walk on the complete graph ∗
Starting from a sequence regarded as a walk through some set of values, we consider the associated loop-erased walk as a sequence of directed edges, with an edge from i to j if the loop erased walk makes a step from i to j. We introduce a coloring of these edges by painting edges with a fixed color as long as the walk does not loop back on itself, then switching to a new color whenever a loop i...
متن کاملThe infinite two-sided loop-erased random walk
The loop-erased random walk (LERW) in Zd, d ≥ 2, dimensions is obtained by erasing loops chronologically from simple random walk. In this paper we show the existence of the two-sided LERW which can be considered as the distribution of the LERW as seen by a point in the “middle” of the path.
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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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 کاملTwo-sided loop-erased random walk in three dimensions
The loop-erased random walk (LERW) in three dimensions is obtained by erasing loops chronologically from simple random walk. In this paper we show the existence of the two-sided LERW which can be considered as the distribution of the LERW as seen by a point in the “middle” of the path.
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