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Hyperbolic random walks

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

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.

Key words

  • Hyperbolic plane
  • random walk
  • invariance principle
  • non Fuchsian group
  • hypergroup
  • stable process

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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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