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Hyperbolic random walks

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Séminaire de Probabilités XLI

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1934))

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Abstract

Although the hyperbolic r.w. defined on a regular hyperbolic planar grid satisfies an invariance principle, as we shall see, the picture radically differs from the Euclidean setting: the infinite grid is the whole space when the step is too small. We also give a radial discretization of Bochner’s subordinated hyperbolic Brownian motions.

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Author information

Authors and Affiliations

  1. Laboratoire Nicolas Oresme, Université de Caen, BP 5186, F-14032, Caen Cedex, France

    Jean-Claude Gruet

Authors
  1. Jean-Claude Gruet
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Editor information

Editors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Boîte courrier I88 4, place Jussieu, 75252, Paris cedex 05, France

    Catherine Donati-Martin

  2. Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 7, rue René Descartes, 67084, Strasbourg cedex, France

    Michel Émery

  3. Laboratoire de Mathématiques Bâtiment Fermat, Université Versailles-Saint-Quentin, 45, avenue des Etats-Unis, 78035, Versailles cedex, France

    Alain Rouault

  4. UFR Sciences et techniques, Université de Besançon, 16, route de Gray, 25030, Besançon cedex, France

    Christophe Stricker

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Gruet, JC. (2008). Hyperbolic random walks. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol 1934. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77913-1_14

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