Trees within trees II: Nested Fragmentations

Abstract : Similarly as in (Blancas et al. 2018) where nested coalescent processes are studied, we generalize the definition of partition-valued homogeneous Markov fragmentation processes to the setting of nested partitions, i.e. pairs of partitions $(\zeta,\xi)$ where $\zeta$ is finer than $\xi$. As in the classical univariate setting, under exchangeability and branching assumptions, we characterize the jump measure of nested fragmentation processes, in terms of erosion coefficients and dislocation measures. Among the possible jumps of a nested fragmentation , three forms of erosion and two forms of dislocation are identified – one of which being specific to the nested setting and relating to a bivariate paintbox process.
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Pré-publication, Document de travail
37 pages, 6 figures. 2018
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https://hal.archives-ouvertes.fr/hal-01842036
Contributeur : Jean-Jil Duchamps <>
Soumis le : mardi 17 juillet 2018 - 18:19:08
Dernière modification le : vendredi 4 janvier 2019 - 17:33:38
Document(s) archivé(s) le : jeudi 18 octobre 2018 - 16:02:23

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  • HAL Id : hal-01842036, version 1
  • ARXIV : 1807.05951

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Jean-Jil Duchamps. Trees within trees II: Nested Fragmentations. 37 pages, 6 figures. 2018. 〈hal-01842036〉

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