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


 
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1. Title Title of document Moderate Deviations in a Random Graph and for the Spectrum of Bernoulli Random Matrices
 
2. Creator Author's name, affiliation, country Hanna Döring; Ruhr-Universität Bochum; Germany
 
2. Creator Author's name, affiliation, country Peter Eichelsbacher; Ruhr-Universität Bochum; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) moderate deviations; random graphs; concentration inequalities; U-statistics; Markov chains; random matrices
 
3. Subject Subject classification 60F10; 05C80; 62G20; 15A52; 60F05
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Studienstiftung des deutschen Volkes; Deutsche Forschungsgemeinschaft via SFB/TR 12
 
7. Date (YYYY-MM-DD) 2009-12-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/723
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-723
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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