Based on a non-rigorous formalism called the “cavity method”, physicists have put forward
intriguing predictions on phase transitions in diluted mean-field models, in which the …

Diluted mean-field models are graphical models in which the geometry of interactions is
determined by a sparse random graph or hypergraph. Based on a nonrigorous but analytic …

We consider the problem of coloring the vertices of a large sparse random graph with a
given number of colors so that no adjacent vertices have the same color. Using the cavity …

We consider the problem of coloring Erdös-Rényi and regular random graphs of finite
connectivity using q colors. It has been studied so far using the cavity approach within the so …

We study the graph coloring problem over random graphs of finite average connectivity c.
Given a number q of available colors, we find that graphs with low connectivity admit almost …

We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where
the coupling constant J_ ij (β) J ij (β) for the edge ij ij on the complete graph is given by J_ ij …

Diluted mean-field models are spin systems whose geometry of interactions is induced by a
sparse random graph or hypergraph. Such models play an eminent role in the statistical …

The aim of this paper is to prove central limit theorems with respect to the annealed measure
for the magnetization rescaled by $\sqrt {N} $ of Ising models on random graphs. More …

Abstract For 0< p< 1 and q> 0 let Gq (n, p) denote the random graph with vertex set n= 1,…,
n such that, for each graph G on n with e (G) edges and c (G) components, the probability …

The “classical” random graph models, in particular G (n, p), are “homogeneous,” in the
sense that the degrees (for example) tend to be concentrated around a typical value. Many …