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Asymptotic Laws for Nonconservative Self-similar Fragmentations


 
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1. Title Title of document Asymptotic Laws for Nonconservative Self-similar Fragmentations
 
2. Creator Author's name, affiliation, country Jean Bertoin; Université Paris VI
 
2. Creator Author's name, affiliation, country Alexander V. Gnedin; Rijksuniversiteit Utrecht, The Netherlands
 
3. Subject Discipline(s)
 
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4. Description Abstract We consider a self-similar fragmentation process in which the generic particle of mass $x$ is replaced by the offspring particles at probability rate $x^\alpha$, with positive parameter $\alpha$. The total of offspring masses may be both larger or smaller than $x$ with positive probability. We show that under certain conditions the typical mass in the ensemble is of the order $t^{-1/\alpha}$ and that the empirical distribution of masses converges to a random limit which we characterise in terms of the reproduction law.
 
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6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2004-07-30
 
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/215
 
10. Identifier Digital Object Identifier 10.1214/EJP.v9-215
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 9
 
12. Language English=en
 
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