Regularity of formation of dust in self-similar fragmentations

被引：12

作者：

Haas, B

机构：

[1] Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75013 Paris, France

[2] CNRS, UMR 7599, F-75013 Paris, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2004年 / 40卷 / 04期

关键词：

fragmentation; self-similarity; loss of mass to dust; Lebesgue density; Holder-continuity;

D O I：

10.1016/j.anihbp.2003.11.002

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In self-similar fragmentations with a negative index, fragments split even faster as their mass is smaller, so that the fragmentation runs away and some mass is reduced to dust. Our purpose is to investigate the regularity of this formation of dust. Let M(t) denote the mass of dust at time t. We give some sufficient and some necessary conditions for the measure dM to be absolutely continuous. In case of absolute continuity, we obtain an approximation of the density by functions of small fragments. We also study the Hausdorff dimension of dM and of its support, as well as the Holder-continuity of the dust's mass M. (C) 2004 Elsevier SAS. All rights reserved.

引用

页码：411 / 438

页数：28

共 24 条

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