The Annals of Applied Probability

A Berry–Esseen bound with applications to vertex degree counts in the Erdős–Rényi random graph

Larry Goldstein

Full-text: Open access

Abstract

Applying Stein’s method, an inductive technique and size bias coupling yields a Berry–Esseen theorem for normal approximation without the usual restriction that the coupling be bounded. The theorem is applied to counting the number of vertices in the Erdős–Rényi random graph of a given degree.

Article information

Source
Ann. Appl. Probab., Volume 23, Number 2 (2013), 617-636.

Dates
First available in Project Euclid: 12 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1360682024

Digital Object Identifier
doi:10.1214/12-AAP848

Mathematical Reviews number (MathSciNet)
MR3059270

Zentralblatt MATH identifier
1278.60048

Subjects
Primary: 60F05: Central limit and other weak theorems 60C05: Combinatorial probability 05C80: Random graphs [See also 60B20]

Keywords
Stein’s method size bias coupling inductive method random graphs

Citation

Goldstein, Larry. A Berry–Esseen bound with applications to vertex degree counts in the Erdős–Rényi random graph. Ann. Appl. Probab. 23 (2013), no. 2, 617--636. doi:10.1214/12-AAP848. https://projecteuclid.org/euclid.aoap/1360682024


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References

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