Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

We study the problem of satisfiability of randomly chosen clauses, each with K Boolean
variables. Using the cavity method at zero temperature, we find the phase diagram for the K …

Physical processes have inspired many optimization heuristics. Most famously, variants of
simulated annealing and genetic algorithms are widely used tools for the exploration of …

Using the cavity equations of Mézard, Parisi, and Zecchina Science 297 (2002), 812;
Mézard and Zecchina, Phys Rev E 66 (2002), 056126 we derive the various threshold …

We derive analytical solutions for p-spin models with finite connectivity at zero temperature.
These models are the statistical mechanics equivalent of p-XORSAT problems in theoretical …

We present a detailed study of the phase diagram of the Ising model in random graphs with
arbitrary degree distribution. By using the replica method we compute exactly the value of …

Recently, it has been recognized that phase transitions play an important role in the
probabilistic analysis of combinatorial optimization problems. However, there are in fact …

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 …

In this paper we generalize to the case of diluted spin models and random combinatorial
optimization problems a technique recently introduced by Guerra (cond-mat/0205123) to …

The field of granular physics has burgeoned since its development in the late 1980s, when
physicists first began to use statistical mechanics to study granular media. They are …