Displaying similar documents to “Dislocation measure of the fragmentation of a general Lévy tree”

Morphospace: Measurement, Modeling, Mathematics, and Meaning

N. Khiripet, R. Viruchpintu, J. Maneewattanapluk, J. Spangenberg, J.R. Jungck (2010)

Mathematical Modelling of Natural Phenomena

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Artists have long recognized that trees are self-similar across enormous differences in magnitudes; i.e., they share a common fractal structure - a trunk subdivides into branches which subdivide into more branches which eventually terminate in leaves, flowers, fruits, etc. Artistid Lindenmayer (1971, 1975, 1989, 1990) invented a mathematics based on graph grammar rewriting systems to describe such iteratively branching structures; these were named in honor of him and are referred to...

Dislocation measure of the fragmentation of a general Lévy tree

Guillaume Voisin (2012)

ESAIM: Probability and Statistics

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Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [R. Abraham and L. Serlet, (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, ...

The triangles method to build -trees from incomplete distance matrices

Alain Guénoche, Bruno Leclerc (2010)

RAIRO - Operations Research

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A method to infer -trees (valued trees having as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2-3 distance values between the elements of , if they fulfill some explicit conditions. This construction is based on the mapping between -tree and a weighted generalized 2-tree spanning .

Random real trees

Jean-François Le Gall (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real trees called stable trees, which generalize the CRT. We review several important results concerning...