Moderate Deviations via Cumulants
By Hanna Döring, Peter Eichelsbacher. 2010
70 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c307474fbac0030475d146d8d94794477c1569dc
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In Applied Mathematics
In Discrete Mathematics and Combinatorics
In Statistics and Probability
Citations in the corpus
- Mod-ϕ Convergence (2016, background): “In [DE13b], Döring and Eichelsbacher analysed Janson’s original proof and established that the theorem holded with Cr = (2e)r(r!)3.”