@article{ECP1190,
author = {Ioannis Kontoyiannis and Mokshay Madiman},
title = {Measure Concentration for Compound Poisson Distributions},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {11},
year = {2006},
keywords = {Compound Poisson measure; measure concentration; entropy method; logarithmic-Sobolev inequality; polynomial tails; Herbst argument},
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).},
pages = {no. 5, 45--57},
issn = {1083-589X},
doi = {10.1214/ECP.v11-1190},
url = {http://ecp.ejpecp.org/article/view/1190}}