On the re-rooting invariance property of Lev́y trees.
Duquesne, Thomas, Le Gall, Jean-Francois (2009)
Electronic Communications in Probability [electronic only]
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Duquesne, Thomas, Le Gall, Jean-Francois (2009)
Electronic Communications in Probability [electronic only]
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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...
Itai Benjamini, Yuval Peres (1992)
Annales de l'I.H.P. Probabilités et statistiques
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Eric Fekete (2010)
ESAIM: Probability and Statistics
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We consider branching random walks with binary search trees as underlying trees. We show that the occupation measure of the branching random walk, up to some scaling factors, converges weakly to a deterministic measure. The limit depends on the stable law whose domain of attraction contains the law of the increments. The existence of such stable law is our fundamental hypothesis. As a consequence, using a one-to-one correspondence between binary trees and plane trees, we give a description...
Wolfgang Woess (1995)
Monatshefte für Mathematik
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Le Gall, Jean-François (2005)
Probability Surveys [electronic only]
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Zhan Shi (2011)
ESAIM: Proceedings
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These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to the main part, Section 3, where branching...
Kuba, Markus, Panholzer, Alois (2006)
The Electronic Journal of Combinatorics [electronic only]
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