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Measure Concentration for Compound Poisson Distributions


 
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1. Title Title of document Measure Concentration for Compound Poisson Distributions
 
2. Creator Author's name, affiliation, country Ioannis Kontoyiannis; Division of Applied Mathematics, Brown University
 
2. Creator Author's name, affiliation, country Mokshay M Madiman; Division of Applied Mathematics, Brown University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Compound Poisson measure; measure concentration; entropy method; logarithmic-Sobolev inequality; polynomial tails; Herbst argument
 
3. Subject Subject classification 60E07; 60E15; 46N30; 39B62
 
4. Description Abstract We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive new concentration bounds. When the measure of interest does not have finite exponential moments, these bounds exhibit optimal {em polynomial} decay. Simple new proofs are also given for earlier results of Houdr{'e} (2002) and Wu (2000).
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Sloan Foundation and NSF
 
7. Date (YYYY-MM-DD) 2006-05-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1190
 
10. Identifier Digital Object Identifier 10.1214/ECP.v11-1190
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 11
 
12. Language English=en
 
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