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- W2783809158 abstract "Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(mathcal {T},d,r,p)$, where $(mathcal {T},d)$ is a tree-like metric space, $rin mathcal {T}$ is a distinguished root, and $p$ is a probability measure on this space. Intuitively, these trees have a combinatorial “underlying branching structure” implied by their topology but otherwise independent of the metric $d$. We explore various ways of making this rigorous, using the weight $p$ to do so without losing the fractal complexity possible in continuum trees. We introduce a notion of mass-structural equivalence and show that two rooted, weighted $mathbb {R}$-trees are equivalent in this sense if and only if the discrete hierarchies derived by i.i.d. sampling from their weights, in a manner analogous to Kingman’s paintbox, have the same distribution. We introduce a family of trees, called “interval partition trees” that serve as representatives of mass-structure equivalence classes, and which naturally represent the laws of the aforementioned hierarchies." @default.
- W2783809158 created "2018-01-26" @default.
- W2783809158 creator A5011298709 @default.
- W2783809158 date "2020-01-01" @default.
- W2783809158 modified "2023-09-25" @default.
- W2783809158 title "Exchangeable hierarchies and mass-structure of weighted real trees" @default.
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- W2783809158 doi "https://doi.org/10.1214/20-ejp522" @default.
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