Self-similar fragmentations derived from the stable tree I

By Grégory Miermont. 2003

88 citations recorded by the source corpus.

AbstractThe basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process (F−(t),t≥0) out of this tree by removing the vertices located under height t. Thanks to a self-similarity property of the stable tree, we show that the fragmentation process is also self-similar. The semigroup and other features of the fragmentation are given explicitly. Asymptotic results are given, as well as a couple of related results on continuous-state branching processes.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0cf271b08a213a4bd4659b853c1818553f845423

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

A new family of Markov branching trees: the alpha-gamma model (2008, background): “It is related to the stable tree of Duquesne and Le Gall [7], see also [21] and Section 3.”
The asymptotic behavior of fragmentation processes (2003, background): “We further refer to [5] for an alternative construction of the same fragmentation from the Brownian excursion, to [7] for another binary and non discrete self-similar fragmentation with negative index α = −1/2, which is also naturally connected to the Brownian excursion, and to [23,24] for other mor”