Displaying similar documents to “Random Walks and Trees”

Einstein relation for biased random walk on Galton–Watson trees

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.

Branching random walks on binary search trees: convergence of the occupation measure

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...

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...

Convergence of simple random walks on random discrete trees to brownian motion on the continuum random tree

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...