Moderate Deviations via Cumulants

Hanna Döring () and Peter Eichelsbacher ()
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Hanna Döring: Technische Universität Berlin
Peter Eichelsbacher: Ruhr-Universität Bochum

Journal of Theoretical Probability, 2013, vol. 26, issue 2, 360-385

Abstract: Abstract The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations probabilities due to Rudzkis, Saulis, and Statulevičius. The examples of random objects we treat include dependency graphs, subgraph-counting statistics in Erdös–Rényi random graphs and U-statistics. Moreover, we prove moderate deviation principles for certain statistics appearing in random matrix theory, namely characteristic polynomials of random unitary matrices and the number of particles in a growing box of random determinantal point processes such as the number of eigenvalues in the GUE or the number of points in Airy, Bessel, and sine random point fields.

Keywords: Moderate deviations; Cumulants; Large deviation probabilities; Dependency graphs; Random graphs; U-statistics; Characteristic polynomials; Random matrix ensembles; Determinantal point processes; 60F10; 05C80; 62G20; 60B20 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10959-012-0437-0

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