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Stationary Gaussian random fields on hyperbolic spacesand on Euclidean spheres∗∗∗

Published online by Cambridge University Press:  03 July 2012

S. Cohen and
M. A. Lifshits
S. Cohen
Affiliation:
Universitéde Toulouse, Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse, France. Serge.Cohen@math.univ-toulouse.fr
M. A. Lifshits
Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya pl., 2, 198504, Stary Peterhof, Russia; lifts@mail.rcom.ru

Abstract

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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.

Keywords

Hyperbolic spaceRandom fieldsLévy’s Brownian field.

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 16 , 2012, pp. 165 - 221
Copyright
© EDP Sciences, SMAI, 2012

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