In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics and, in physics, quantum field theory. It is intimately connected to the uniform spanning tree, a model for a random tree. See also random walk for more general treatment of this topic.
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... If denotes the expected number of vertices in the loop-erased random walk until it gets to a distance of r, then where ε, c and C are some positive numbers (the ...
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