We present a complete analytical solution of a system of Potts spins on a random k-regular graph in both the canonical and microcanonical ensembles, using the Large Deviation Cavity Method (LDCM). The solution is shown to be composed of three different branches, resulting in a non-concave...

The aim of this paper is to use non-asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning principle for thin sets). Applications to stochastic mechanics and calibration problems for diffusion...