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Approximation by the Dickman Distribution and Quasi-Logarithmic Combinatorial Structures


 
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1. Title Title of document Approximation by the Dickman Distribution and Quasi-Logarithmic Combinatorial Structures
 
2. Creator Author's name, affiliation, country Andrew D Barbour; Universität Zürich; Switzerland
 
2. Creator Author's name, affiliation, country Bruno Nietlispach; Universität Zürich; Switzerland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Logarithmic combinatorial structures; Dickman's distribution; Mineka coupling
 
3. Subject Subject classification 60C05; 60F05; 05A16
 
4. Description Abstract Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavaré (2003). In order to obtain asymptotic approximations to their component spectrum, it is necessary first to establish an approximation to the sum of an associated sequence of independent random variables in terms of the Dickman distribution. This in turn requires an argument that refines the Mineka coupling by incorporating a blocking construction, leading to exponentially sharper coupling rates for the sums in question. Applications include distributional limit theorems for the size of the largest component and for the vector of counts of the small components in a quasi-logarithmic combinatorial structure.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Schweizerischer Nationalfonds Projekt Nr. 20--107935/1.
 
7. Date (YYYY-MM-DD) 2011-05-04
 
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/881
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-881
 
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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