Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years, considerable progress has been achieved by viewing these distributions as Gibbs measures and applying to their study heuristic tools from statistical physics. We review this approach and provide some results towards a rigorous treatment of these problems.
Publié le : 2010-07-15
Classification:
Random graphs,
Ising model,
Gibbs measures,
phase transitions,
spin models,
local weak convergence
@article{1271770268,
author = {Dembo, Amir and Montanari, Andrea},
title = {Gibbs measures and phase transitions on sparse random graphs},
journal = {Braz. J. Probab. Stat.},
volume = {24},
number = {1},
year = {2010},
pages = { 137-211},
language = {en},
url = {http://dml.mathdoc.fr/item/1271770268}
}
Dembo, Amir; Montanari, Andrea. Gibbs measures and phase transitions on sparse random graphs. Braz. J. Probab. Stat., Tome 24 (2010) no. 1, pp. 137-211. http://gdmltest.u-ga.fr/item/1271770268/