A note on the distribution of the extreme degrees of a random graph via the Stein-Chen method

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https://link.springer.com/article/10.1007/s11009-024-10091-0

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http://hdl.handle.net/11603/24771
 https://doi.org/10.1007/s11009-024-10091-0

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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https://orcid.org/0000-0003-2888-674X

Date

2024-07-02

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journal articles
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Citation of Original Publication

Malinovsky, Yaakov. “A Note on the Distribution of the Extreme Degrees of a Random Graph via the Stein-Chen Method.” Methodology and Computing in Applied Probability 26, no. 3 (July 2, 2024): 22. https://doi.org/10.1007/s11009-024-10091-0.

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Attribution 4.0 International

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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. 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.