September 2015 Distance between two random k-out digraphs, with and without preferential attachment
Nicholas R. Peterson, Boris Pittel
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Adv. in Appl. Probab. 47(3): 858-879 (September 2015). DOI: 10.1239/aap/1444308885


A random k-out mapping (digraph) on [n] is generated by choosing k random images of each vertex one at a time, subject to a 'preferential attachment' rule: the current vertex selects an image i with probability proportional to a given parameter α = α(n) plus the number of times i has already been selected. Intuitively, the larger α becomes, the closer the resulting k-out mapping is to the uniformly random k-out mapping. We prove that α = Θ(n1/2) is the threshold for α growing 'fast enough' to make the random digraph approach the uniformly random digraph in terms of the total variation distance. We also determine an exact limit for this distance for the α = β n1/2 case.


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Nicholas R. Peterson. Boris Pittel. "Distance between two random k-out digraphs, with and without preferential attachment." Adv. in Appl. Probab. 47 (3) 858 - 879, September 2015.


Published: September 2015
First available in Project Euclid: 8 October 2015

zbMATH: 1325.05068
MathSciNet: MR3406611
Digital Object Identifier: 10.1239/aap/1444308885

Primary: 05C80
Secondary: 60C05 , 60F05

Keywords: k-out digraphs , local limit theorem , preferential attachment , random digraphs , Random graphs , total variation distance , uniform

Rights: Copyright © 2015 Applied Probability Trust


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Vol.47 • No. 3 • September 2015
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