a1 Universitéde Toulouse, Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse, France. [email protected]
a2 Department of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya pl., 2, 198504, Stary Peterhof, Russia; [email protected]
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.
(Received July 6 2009)
(Online publication July 3 2012)
Mathematics Subject Classification:
∗ 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.