Subdiffusive behavior of random walk on a random cluster
Harry Kesten (1986)
Annales de l'I.H.P. Probabilités et statistiques
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Harry Kesten (1986)
Annales de l'I.H.P. Probabilités et statistiques
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Takacs, Christiane (1997)
Electronic Journal of Probability [electronic only]
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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...
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...
Nina Gantert, Yueyun Hu, Zhan Shi (2011)
Annales de l'I.H.P. Probabilités et statistiques
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Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope − , where denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when → 0, this probability decays like exp{−(+o(1)) / 1/2}, where is a positive constant...
Quansheng Liu (1996-1997)
Publications mathématiques et informatique de Rennes
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