Climbing Random Trees.
J.W. Moon (1970)
Aequationes mathematicae
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J.W. Moon (1970)
Aequationes mathematicae
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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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Xavier Messeguer (1997)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Clark, Lane (2005)
International Journal of Mathematics and Mathematical Sciences
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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...
Ivan Gutman, Yeong-Nan Yeh (1993)
Publications de l'Institut Mathématique
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Gerard Ben Arous, Yueyun Hu, Stefano Olla, Ofer Zeitouni (2013)
Annales de l'I.H.P. Probabilités et statistiques
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We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton–Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrarily slow traps.
A. Kośliński (1987)
Applicationes Mathematicae
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