paper

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

arXiv:1208.1558

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.

25 pages

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