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Applications of size biased couplings for concentration of measures

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Applications of size biased couplings for concentration of measures
2.	Creator	Author's name, affiliation, country	Subhankar Ghosh; University of Southern California
2.	Creator	Author's name, affiliation, country	Larry Goldstein; University of Southern California
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	Let $Y$ be a nonnegative random variable with mean $\mu$ and finite positive variance $\sigma^2$, and let $Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by $$ E[Yf(Y)]=\mu E f(Y^s) \quad \mbox{for all functions $f$ for which these expectations exist.} $$ Under a variety of conditions on the coupling of $Y$ and $Y^s$, including combinations of boundedness and monotonicity, concentration of measure inequalities such as $$ P\left(\frac{Y-\mu}{\sigma}\ge t\right)\le \exp\left(-\frac{t^2}{2(A+Bt)}\right) \quad \mbox{for all $t \ge 0$} $$ are shown to hold for some explicit $A$ and $B$ in \cite{cnm}. Such concentration of measure results are applied to a number of new examples: the number of relatively ordered subsequences of a random permutation, sliding window statistics including the number of $m$-runs in a sequence of coin tosses, the number of local maxima of a random function on a lattice, the number of urns containing exactly one ball in an urn allocation model, and the volume covered by the union of $n$ balls placed uniformly over a volume $n$ subset of $\mathbb{R}^d$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-01-23
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/1605
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1605
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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