Conditional limit theorems for branching processes.
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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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...
Takács, Lajos (1991)
Journal of Applied Mathematics and Stochastic Analysis
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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 Croydon (2008)
Annales de l'I.H.P. Probabilités et statistiques
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In this article it is shown that the brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete -vertex ordered graph trees whose search-depth functions converge to the brownian excursion as →∞. We prove both a quenched version (for typical realisations of the trees) and an annealed version (averaged over all realisations of the trees) of our main result. The assumptions of the article cover the important example of simple random...
Duquesne, Thomas, Le Gall, Jean-Francois (2009)
Electronic Communications in Probability [electronic only]
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Takacs, Christiane (1997)
Electronic Journal of Probability [electronic only]
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