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

2012/08/08 by Nathan Ross, Ross, Nathan · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1208.1558

25 pages

arxiv created 2012/08/08 · arxiv updated 2012/08/09

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 infinity. 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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