Distribution of sizes of erased loops for loop-erased random walks

Dhar, Deepak; Dhar, Abhishek

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/4506

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DC Field	Value	Language
dc.contributor.author	Dhar, Deepak	-
dc.contributor.author	Dhar, Abhishek	-
dc.date.accessioned	2012-05-23T03:43:38Z	-
dc.date.available	2012-05-23T03:43:38Z	-
dc.date.issued	1997-03	-
dc.identifier.citation	Physical Review E, 1997, Vol.55, pR2093	en
dc.identifier.issn	1539-3755	-
dc.identifier.issn	1550-2376 (Online)	-
dc.identifier.uri	http://hdl.handle.net/2289/4506	-
dc.description	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)	en
dc.description.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.	en
dc.language.iso	en	en
dc.publisher	American Physical Society	en
dc.relation.uri	http://arxiv.org/abs/cond-mat/9704026	en
dc.relation.uri	http://dx.doi.org/10.1103/PhysRevE.55.R2093	en
dc.relation.uri	http://adsabs.harvard.edu/abs/1997PhRvE..55.2093D	en
dc.rights	1997 The American Physical Society	en
dc.title	Distribution of sizes of erased loops for loop-erased random walks	en
dc.type	Article	en
Appears in Collections:	Research Papers (TP)

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