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- W1995689580 abstract "Let (G n ) =1 ∞ be a sequence of finite graphs, and let Y t be the length of a loop-erased random walk on G n after t steps. We show that for a large family of sequences of finite graphs, which includes the case in which G n is the d-dimensional torus of size-length n for d≥4, the process (Y t ) =0 ∞ , suitably normalized, converges to the Rayleigh process introduced by Evans, Pitman, and Winter. Our proof relies heavily on ideas of Peres and Revelle, who used loop-erased random walks to show that the uniform spanning tree on large finite graphs converges to the Brownian continuum random tree of Aldous." @default.
- W1995689580 created "2016-06-24" @default.
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- W1995689580 date "2007-10-19" @default.
- W1995689580 modified "2023-10-18" @default.
- W1995689580 title "Loop-Erased Random Walk on Finite Graphs and the Rayleigh Process" @default.
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- W1995689580 doi "https://doi.org/10.1007/s10959-007-0125-7" @default.
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