Average properties of random walks on Galton-Watson trees
Dayue Chen (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Dayue Chen (1997)
Annales de l'I.H.P. Probabilités et statistiques
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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...
Volkov, Stanislav (2003)
Electronic Journal of Probability [electronic only]
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Marchal, Philippe (1998)
Electronic Communications in Probability [electronic only]
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Zerner, Martin P.W. (2007)
Electronic Communications in Probability [electronic only]
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Takács, Lajos (1993)
Journal of Applied Mathematics and Stochastic Analysis
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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...
Flaxman, Abraham D. (2007)
The Electronic Journal of Combinatorics [electronic only]
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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.