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A Central Limit Theorem for Random Ordered Factorizations of Integers


 
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1. Title Title of document A Central Limit Theorem for Random Ordered Factorizations of Integers
 
2. Creator Author's name, affiliation, country Hsien-Kuei Hwang; Academia Sinica; China
 
2. Creator Author's name, affiliation, country Svante Janson; Uppsala University; Sweden
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Tauberian theorems; asymptotic normality; ordered factorizations; method of moments; Dirichlet series
 
3. Subject Subject classification 11N80; 11N37; 11K65; 11N60; 11M45; 60F05
 
4. Description Abstract

Write an integer as finite products of ordered factors belonging to a given subset $\mathcal{P}$ of integers larger than one. A very general central limit theorem is derived for the number of ordered factors in random factorizations for any subset $\mathcal{P}$ containing at least two elements. The method of proof is very simple and relies in part on Delange’s Tauberian theorems and an interesting Tauberian technique for handling Dirichlet series associated with odd centered moments.

An erratum is available in EJP volume 18 paper 16
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Council, ROC; Institut Mittag-Leffler
 
7. Date (YYYY-MM-DD) 2011-02-16
 
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/858
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-858
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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