Displaying similar documents to “Convergence of simple random walks on random discrete trees to brownian motion on the continuum random tree”

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...

Invariance principles for spatial multitype Galton–Watson trees

Grégory Miermont (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We prove that critical multitype Galton–Watson trees converge after rescaling to the brownian continuum random tree, under the hypothesis that the offspring distribution is irreducible and has finite covariance matrices. Our study relies on an ancestral decomposition for marked multitype trees, and an induction on the number of types. We then couple the genealogical structure with a spatial motion, whose step distribution may depend on the structure of the tree in a local way, and show...