Moderate deviations in random graphs and Bernoulli random matrices

Details Moderate deviations in random graphs and Bernoulli random matrices Moderate deviations in random graphs and Bernoulli random matrices

2009-01-21

arxiv.org/abs/0901.3246v1

Electronic Journal of Probability, Vol. 14, 2009, Paper no. 92, 2636-2656

Mathematics

Probability

23 pages

Scientific paper

We prove a moderate deviation principle for subgraph count statistics of Erdos-Renyi random graphs. This is equivalent in showing a 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 Gaertner-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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