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.
Mots clés : hyperbolic space, random fields, Lévy's brownian field
@article{PS_2012__16__165_0,
author = {Cohen, S. and Lifshits, M. A.},
title = {Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres},
journal = {ESAIM: Probability and Statistics},
pages = {165--221},
publisher = {EDP-Sciences},
volume = {16},
year = {2012},
doi = {10.1051/ps/2011105},
mrnumber = {2946126},
zbl = {1275.60038},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2011105/}
}
TY - JOUR AU - Cohen, S. AU - Lifshits, M. A. TI - Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres JO - ESAIM: Probability and Statistics PY - 2012 SP - 165 EP - 221 VL - 16 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2011105/ DO - 10.1051/ps/2011105 LA - en ID - PS_2012__16__165_0 ER -
%0 Journal Article %A Cohen, S. %A Lifshits, M. A. %T Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres %J ESAIM: Probability and Statistics %D 2012 %P 165-221 %V 16 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2011105/ %R 10.1051/ps/2011105 %G en %F PS_2012__16__165_0
Cohen, S.; Lifshits, M. A. Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 165-221. doi : 10.1051/ps/2011105. http://www.numdam.org/articles/10.1051/ps/2011105/
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