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Lithuanian Mathematical Journal

, Volume 59, Issue 4, pp 437–468 | Cite as

Local probabilities of randomly stopped sums of power-law lattice random variables

  • Mindaugas BloznelisEmail author
Article
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Abstract

Let X1 and N ≥ 0 be integer-valued power-law random variables. For a randomly stopped sum SN = X1+⋯+XN of independent and identically distributed copies of X1, we establish a first-order asymptotics of the local probabilities P(SN = t) as t → +1 ∞. Using this result, we show the scaling k, 0 ≤ δ ≤ 1, of the local clustering coefficient (of a randomly selected vertex of degree k) in a power-law affiliation network.

Keywords

randomly stopped sum local probabilities power law clustering coefficient random intersection graph 

MSC

60G50 60F10 90B15 

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Computer Science, Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania

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