On the size of a maximal induced tree in a random graph
Michał Karoński, Zbigniew Palka (1980)
Mathematica Slovaca
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Michał Karoński, Zbigniew Palka (1980)
Mathematica Slovaca
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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...
Michał Karoński, Zbigniew Palka (1981)
Mathematica Slovaca
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A. Meir, J.W. Moon (1981)
Aequationes mathematicae
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Zbigniew Pałka (1982)
Colloquium Mathematicae
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Takács, Lajos (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Takacs, Christiane (1997)
Electronic Journal of Probability [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.
Z. Palka (1982)
Applicationes Mathematicae
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