Electronic Journal of Probability

Moderate Deviations in a Random Graph and for the Spectrum of Bernoulli Random Matrices

Hanna Döring and Peter Eichelsbacher

Full-text: Open access

Abstract

We prove the moderate deviation principle for subgraph count statistics of Erdös-Rényi random graphs. This is equivalent in showing the moderate deviation principle for the trace of a power of a Bernoulli random matrix. It is done via an estimation of the log-Laplace transform and the Gärtner-Ellis theorem. We obtain upper bounds on the upper tail probabilities of the number of occurrences of small subgraphs. The method of proof is used to show supplemental moderate deviation principles for a class of symmetric statistics, including non-degenerate U-statistics with independent or Markovian entries.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 92, 2636-2656.

Dates
Accepted: 12 December 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819553

Digital Object Identifier
doi:10.1214/EJP.v14-723

Mathematical Reviews number (MathSciNet)
MR2570014

Zentralblatt MATH identifier
1193.60032

Subjects
Primary: 60F10: Large deviations
Secondary: 05C80: Random graphs [See also 60B20] 62G20: Asymptotic properties 15A52 60F05: Central limit and other weak theorems

Keywords
moderate deviations random graphs concentration inequalities U-statistics Markov chains random matrices

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Döring, Hanna; Eichelsbacher, Peter. Moderate Deviations in a Random Graph and for the Spectrum of Bernoulli Random Matrices. Electron. J. Probab. 14 (2009), paper no. 92, 2636--2656. doi:10.1214/EJP.v14-723. https://projecteuclid.org/euclid.ejp/1464819553


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