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Comportement asymptotique des fonctions harmoniques sur les arbres

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Séminaire de Probabilités XXXIV

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1729))

Abstract

Considering a random walk on an infinite tree, we suppose that transition probabilities are “reasonnable”, id est that they are bounded between two constants taken in (0, 1/2). It is shown that, for a given harmonic function on the tree, properties of radial convergence, radial boundedness, finiteness of radial energy and corresponding stochastic notions are all equivalent at almost each point of the geometric boundary. The idea of the proof comes from an analoguous result on Riemannian manifolds of pinched negative curvature due to the author.

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Authors and Affiliations

  1. Institut Fourier UMR 5582 CNRS-UJF UFR de Mathématiques, Université de Grenoble I, B.P. 74, 38402, SAINT-MARTIN D’HÈRES CEDEX, France

    Frédéric Mouton

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  1. Frédéric Mouton
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Jacques Azéma Michel Ledoux Michel Émery Marc Yor

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© 2000 Springer-Verlag

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Mouton, F. (2000). Comportement asymptotique des fonctions harmoniques sur les arbres. In: Azéma, J., Ledoux, M., Émery, M., Yor, M. (eds) Séminaire de Probabilités XXXIV. Lecture Notes in Mathematics, vol 1729. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103813

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  • DOI: https://doi.org/10.1007/BFb0103813

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67314-9

  • Online ISBN: 978-3-540-46413-6

  • eBook Packages: Springer Book Archive

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