Discretization Methods for Homogeneous Fragmentations

By Jean Bertoin, Alain Rouault. 2004

60 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0c57bed93337903b4891274b03388e1733c7572e

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Multifractal spectra and precise rates of decay in homogeneous fragmentations (2006, background): “Bertoin and Rouault (Corollary 2 in [11]) proved that”
The Seneta–Heyde scaling for the branching random walk (2011, background): “It can be adapted in other situations, for example, in the study of fragmentation processes (Bertoin and Rouault [6], Berestycki, Harris and Kyprianou [5]).”
Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions (2008, methodology): “Proposition 18 using partition-valued fragmentation processes and stopping lines; see [4, 19].”
Spinal partitions and invariance under re-rooting of continuum random trees (2007, methodology): “In the fragmentation context, decomposing the trees/processes along the spine is a useful tool, which has been used to obtain results on large time asymptotics [11], small time asymptotics [24] and discrete approximations [26].”
Markovian growth-fragmentation processes (2017, background): “time skeletons of homogeneous fragmentations can be viewed as branching random walks; the latter have been studied in depth for more than fours decades and yield many useful informations and techniques relevant to homogeneous fragmentations; see in particular [5].”
Martingales and Profile of Binary Search Trees (2004, unknown): “convergence of the martingales M ′(t, z) and the signs of the limits are proved in [9], and so is the relation EM (∞, z c ) = −EM (∞, z c ) = ∞ .”