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Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres

S. Cohen, M. A. Lifshits (2012)

ESAIM: Probability and Statistics

We recall necessary notions about the geometry and harmonic analysis on a hyperbolic space and provide lecture notes about homogeneous random functions parameterized by this space. The general principles are illustrated by construction of numerous examples analogous to Euclidean case. We also give a brief survey of the fields parameterized by Euclidean spheres. At the end we give a list of important open questions in hyperbolic case.

Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres∗∗∗

S. Cohen, M. A. Lifshits (2012)

ESAIM: Probability and Statistics

We recall necessary notions about the geometry and harmonic analysis on a hyperbolic space and provide lecture notes about homogeneous random functions parameterized by this space. The general principles are illustrated by construction of numerous examples analogous to Euclidean case. We also give a brief survey of the fields parameterized by Euclidean spheres. At the end we give a list of important open questions in hyperbolic case.

Sugli isomorfismi tra spazi di Grassman

Eva Ferrara Dentice, Nicola Melone (1999)

Bollettino dell'Unione Matematica Italiana

In this paper we prove that any incidence-preserving bijection between the line sets of Grassmann spaces is induced by either a collineation or a correlation.

Sur la rigidité de polyèdres hyperboliques en dimension  3 : cas de volume fini, cas hyperidéal, cas fuchsien

Mathias Rousset (2004)

Bulletin de la Société Mathématique de France

Un polyèdre hyperbolique semi-idéal est un polyèdre dont les sommets sont dans l’espace hyperbolique ℍ 3 ou à l’infini. Un polyèdre hyperbolique hyperidéal est, dans le modèle projectif, l’intersection de ℍ 3 avec un polyèdre projectif dont les sommets sont tous en dehors de ℍ 3 et dont toutes les arêtes rencontrent ℍ 3 . Nous classifions les polyèdres semi-idéaux en fonction de leur métrique duale, d’après les résultats de Rivin dans [8] (écrit avec C.D.Hodgson) et [7]. Nous utilisons ce résultat pour retrouver...

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