COMPENSATED FRAGMENTATION PROCESSES AND LIMITS OF DILATED FRAGMENTATIONS

• 成果类型: Article
• 署名作者: Bertoin, Jean
• 署名单位: University of Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP1000
• 发表日期: 2016
• 页码: 1254-1284
• 关键词: branching random-walk; CONVERGENCE; GROWTH; particles; BEHAVIOR

摘要

A new class of fragmentation-type random processes is introduced, in which, roughly speaking, the accumulation of small dislocations which would instantaneously shatter the mass into dust, is compensated by an adequate dilation of the components. An important feature of these compensated fragmentations is that the dislocation measure nu which governs their evolutions has only to fulfill the integral condition integral P(1 - p(1))(2)nu(dp) < infinity, where p = (p(1),...) denotes a generic mass-partition. This is weaker than the necessary and sufficient condition integral P (1 - p(1))nu(dp) < infinity for nu to be the dislocation measure of a homogeneous fragmentation. Our main results show that such compensated fragmentations naturally arise as limits of homogeneous dilated fragmentations, and bear close connections to spectrally negative Levy processes.