On the distribution of the number of vertices in layers of random trees.
Takács, Lajos (1991)
Journal of Applied Mathematics and Stochastic Analysis
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Takács, Lajos (1991)
Journal of Applied Mathematics and Stochastic Analysis
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Takács, Lajos (1993)
Journal of Applied Mathematics and Stochastic Analysis
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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...
Le Gall, Jean-François (2005)
Probability Surveys [electronic only]
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David Aldous, Jim Pitman (1998)
Annales de l'I.H.P. Probabilités et statistiques
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Aldous, David, Miermont, Grégory, Pitman, Jim (2004)
Electronic Journal of Probability [electronic only]
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Kuba, Markus, Panholzer, Alois (2006)
The Electronic Journal of Combinatorics [electronic only]
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Drmota, Michael, Gittenberger, Bernhard (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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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...