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

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

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 se...

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Veröffentlicht in:Methodology and computing in applied probability 2024-09, Vol.26 (3), p.22, Article 22
1. Verfasser: Malinovsky, Yaakov
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Asymptotic methods
Business and Management
Economics
Electrical Engineering
Graph theory
Life Sciences
Mathematics and Statistics
Methods
Random variables
Statistics
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Zusammenfassung: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.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-024-10091-0