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2009 Moderate Deviations in a Random Graph and for the Spectrum of Bernoulli Random Matrices
Hanna Döring, Peter Eichelsbacher
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Electron. J. Probab. 14: 2636-2656 (2009). DOI: 10.1214/EJP.v14-723


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.


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Hanna Döring. Peter Eichelsbacher. "Moderate Deviations in a Random Graph and for the Spectrum of Bernoulli Random Matrices." Electron. J. Probab. 14 2636 - 2656, 2009.


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

zbMATH: 1193.60032
MathSciNet: MR2570014
Digital Object Identifier: 10.1214/EJP.v14-723

Primary: 60F10
Secondary: 05C80 , 15A52 , 60F05 , 62G20

Keywords: Concentration inequalities , Markov chains , Moderate deviations , Random graphs , random matrices , U-statistics

Vol.14 • 2009
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