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Small counts in the infinite occupancy scheme

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1.	Title	Title of document	Small counts in the infinite occupancy scheme
2.	Creator	Author's name, affiliation, country	A. D. Barbour; University of Zurich
2.	Creator	Author's name, affiliation, country	A. V. Gnedin; Utrecht University
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	occupancy problem; normal approximation; poissonization; regular variation
3.	Subject	Subject classification	60F05, 60C05
4.	Description	Abstract	The paper is concerned with the classical occupancy scheme in which balls are thrown independently into infinitely many boxes, with given probability of hitting each of the boxes. We establish joint normal approximation, as the number of balls goes to infinity, for the numbers of boxes containing any fixed number of balls, standardized in the natural way, assuming only that the variances of these counts all tend to infinity. The proof of this approximation is based on a de-Poissonization lemma. We then review sufficient conditions for the variances to tend to infinity. Typically, the normal approximation does not mean convergence. We show that the convergence of the full vector of counts only holds under a condition of regular variation, thus giving a complete characterization of possible limit correlation structures.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Schweizerischer Nationalfonds Projekt Nr. 20-117625/1
7.	Date	(YYYY-MM-DD)	2009-02-09
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/608
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-608
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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