A Note on the Distribution of the Extreme Degrees of a Random Graph via the Stein-Chen Method

Yaakov Malinovsky ()
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Yaakov Malinovsky: University of Maryland

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 3, 1-7

Abstract: Abstract We offer an alternative proof, using the Stein-Chen method, of Bollobás’ theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic distribution. The same method also applies in a more general setting where the probability of every pair of vertices being connected by edges depends on the number of vertices.

Keywords: Random graphs; Extremes; Positive dependence; Poisson approximation; Total variation distance; 05C80; 05C07; 62G32 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11009-024-10091-0

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