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Power Laws in Preferential Attachment Graphs and Stein's Method for the Negative Binomial Distribution

Published online by Cambridge University Press:  04 January 2016

Nathan Ross*
Affiliation:
University of California, Berkeley
*
Current address: Department of Mathematics and Statistics, Richard Berry Building, University of Melbourne, VIC 3010, Australia. Email address: [email protected]
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Abstract

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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.

Type
General Applied Probability
Copyright
© Applied Probability Trust 

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