The Largest Fragment of a Homogeneous Fragmentation Process

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• 作者：Andreas Kyprianou ; Francis Lane ; Peter Mörters
• 刊名：Journal of Statistical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：166
• 期：5
• 页码：1226-1246
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9613
• 卷排序：166

文摘

We show that in homogeneous fragmentation processes the largest fragment at time t has size $$\begin{aligned} e^{-t \Phi '(\overline{p})}t^{-\frac{3}{2} (\log \Phi )'(\overline{p})+o(1)}, \end{aligned}$$where \(\Phi \) is the Lévy exponent of the fragmentation process, and \(\overline{p}\) is the unique solution of the equation \((\log \Phi )'(\bar{p})=\frac{1}{1+\bar{p}}\). We argue that this result is in line with predictions arising from the classification of homogeneous fragmentation processes as logarithmically correlated random fields.References1.Addario-Berry, L., Reed, B.: Minima in branching random walks. Ann. Probab. 37(3), 1044–1079 (2009)MathSciNetCrossRefMATHGoogle Scholar2.Aïdékon, E.: Convergence in law of the minimum of a branching random walk. Ann. Probab. 41(3A), 1362–1426 (2013)MathSciNetCrossRefMATHGoogle Scholar3.Aïdékon, E.: The extrenal process in nested conformal loops. 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Probab. 41(5), 3518–3541 (2013)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer Science+Business Media New York 2017Authors and AffiliationsAndreas Kyprianou1Francis Lane1Peter Mörters1Email authorView author's OrcID profile1.Department of Mathematical SciencesUniversity of BathBathUK About this article CrossMark Publisher Name Springer US Print ISSN 0022-4715 Online ISSN 1572-9613 About this journal Reprints and Permissions Article actions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. More information Accept Over 10 million scientific documents at your fingertips