2004/09/28 by Jean Bertoin, JEAN BERTOIN, Alain Rouault +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Algebraic and Geometric Analysis #Homotopy and Cohomology in Algebraic Topology #math.PR #msc:09 #msc:25 #msc:60
paper · pdf · doi:10.1112/s0024610705006423
published as Journal of the London Mathematical Society, Volume 72, Issue 01, août 2005 · 21 pages
arxiv created 2004/09/28 · openalex publication_date 2005/07/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogues of a certain type of branching random walk, which suggests the use of time-discretization to shift known results from the theory of branching random walks to the fragmentation setting. In particular, this yields interesting information about the asymptotic behaviour of fragmentations. On the other hand, homogeneous fragmentations can also be investigated using a powerful technique of discretization of space due to Kingman, namely, the theory of exchangeable partitions of N. Spatial discretization is especially well suited to the direct development for continuous times of the conceptual method of probability tilting of Lyons, Pemantle and Peres.