English

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

Combinatorics 2023-11-20 v4 Probability Statistics Theory Statistics Theory

Abstract

We offer an alternative proof, using the Stein-Chen method, of Bollob\'{a}s' 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

Cite

@article{arxiv.2204.05881,
  title  = {A note on the distribution of the extreme degrees of a random graph via the Stein-Chen method},
  author = {Yaakov Malinovsky},
  journal= {arXiv preprint arXiv:2204.05881},
  year   = {2023}
}

Comments

Small fix