Advances in Applied Probability

Power laws in preferential attachment graphs and Stein's method for the negative binomial distribution

Nathan Ross

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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.

Article information

Source
Adv. in Appl. Probab. Volume 45, Number 3 (2013), 876-893.

Dates
First available in Project Euclid: 30 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.aap/1377868543

Digital Object Identifier
doi:10.1239/aap/1377868543

Mathematical Reviews number (MathSciNet)
MR3102476

Zentralblatt MATH identifier
1273.05205

Subjects
Primary: 05C80: Random graphs [See also 60B20]
Secondary: 60F05: Central limit and other weak theorems 60C05: Combinatorial probability

Keywords
Stein's method negative binomial distribution random graph preferential attachment distributional transformation power law

Citation

Ross, Nathan. Power laws in preferential attachment graphs and Stein's method for the negative binomial distribution. Adv. in Appl. Probab. 45 (2013), no. 3, 876--893. doi:10.1239/aap/1377868543. https://projecteuclid.org/euclid.aap/1377868543


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