| Issue |
ESAIM: PS
Volume 16, 2012
Special Issue: Spring School Mons Random differential equations and Gaussian fields
|
|
|---|---|---|
| Page(s) | 165 - 221 | |
| DOI | https://doi.org/10.1051/ps/2011105 | |
| Published online | 03 July 2012 | |
Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres∗,∗∗
1 Universitéde Toulouse, Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse, France
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2 Department of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya pl., 2, 198504, Stary Peterhof, Russia
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Received: 6 July 2009
Abstract
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.
Mathematics Subject Classification: 60G15 / 60G10 / 51M10
Key words: Hyperbolic space / Random fields / Lévy’s Brownian field.
ANR GDSA and grants NSh-638.2008.1, RFBR 09 − 01 − 12180-ofim.
Most of this work was done when M. Lifshits was invited professor in Université Paul Sabatier.
© EDP Sciences, SMAI, 2012
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