Title:	Distribution of sizes of erased loops for loop-erased random walks
Authors:	Dhar, Deepak Dhar, Abhishek
Issue Date:	Mar-1997
Publisher:	American Physical Society
Citation:	Physical Review E, 1997, Vol.55, pR2093
Abstract:	We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability P(l) of generating a loop of perimeter l is expressible in terms of the probability Pst(l) of forming a loop of perimeter l when a bond is added to a random spanning tree on the same graph by the simple relation P(l)=Pst(l)/l. On d-dimensional hypercubical lattices, P(l) varies as l-σ for large l, where σ=1+2/z for 1<d<4, where z is the fractal dimension of the loop-erased walks on the graph. On recursively constructed fractals with d-tilde<2 this relation is modified to σ=1+2d-bar/(d-tildez), where d-bar is the Hausdorff and d-tilde is the spectral dimension of the fractal.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/4506
ISSN:	1539-3755 1550-2376 (Online)
Alternative Location:	http://arxiv.org/abs/cond-mat/9704026 http://dx.doi.org/10.1103/PhysRevE.55.R2093 http://adsabs.harvard.edu/abs/1997PhRvE..55.2093D
Copyright:	1997 The American Physical Society
Appears in Collections:	Research Papers (TP)

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