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September 2013 Power laws in preferential attachment graphs and Stein's method for the negative binomial distribution
Nathan Ross
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Adv. in Appl. Probab. 45(3): 876-893 (September 2013). DOI: 10.1239/aap/1377868543

Abstract

For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends to ∞. Our proof uses a new formulation of Stein's method for the negative binomial distribution, which stems from a distributional transformation that has the negative binomial distributions as the only fixed points.

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Nathan Ross. "Power laws in preferential attachment graphs and Stein's method for the negative binomial distribution." Adv. in Appl. Probab. 45 (3) 876 - 893, September 2013. https://doi.org/10.1239/aap/1377868543

Information

Published: September 2013
First available in Project Euclid: 30 August 2013

zbMATH: 1273.05205
MathSciNet: MR3102476
Digital Object Identifier: 10.1239/aap/1377868543

Subjects:
Primary: 05C80
Secondary: 60C05, 60F05

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 3 • September 2013
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