Scale-free and Power Law Distributions via Fixed Points and Convergence of (thinning and Conditioning) Transformations

Abstract

In discrete contexts such as the degree distribution for a graph, scale-free has traditionally been defined to be power-law. We propose a reasonable interpretation of scale-free, namely, invariance under the transformation of p-thinning, followed by conditioning on being positive. For each β ∈ (1, 2), we show that there is a unique distribution which is a… (More)

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