We analyze the generalized mean-field q-state Potts model which is obtained by replacing
the usual quadratic interaction function in the mean-field Hamiltonian by a higher power z …

We consider translation-invariant interacting particle systems on the lattice with finite local
state space admitting at least one Gibbs measure as a time-stationary measure. The …

We consider a class of discrete q-state spin models defined in terms of a translation-
invariant quasilocal specification with discrete clock-rotation invariance which have extremal …

In this paper we consider the Glauber dynamics for the one-dimensional Ising model with
dissipation, in a mesoscopic regime obtained by letting inverse temperature and volume go …

We characterize the phase space for the infinite volume limit of a ferromagnetic mean-field
XY model in a random field pointing in one direction with two symmetric values. We …

The Polya urn is the paradigmatic example of a reinforced stochastic process. It leads to a
random (non degenerated) almost sure (as) time-limit. The Friedman urn is a natural …

We provide an example of a discrete-time Markov process on the three-dimensional infinite
integer lattice with Z q-invariant Bernoulli-increments which has as local state space the …

We present a family of interacting stochastic processes introduced in [13] whose individual
dynamics follow a reinforcement updating rule. This is a natural generalization of PCA …

We compute the Hamiltonian and Lagrangian associated to the large deviations of the
trajectory of the empirical distribution for independent Markov processes, and of the …

We consider stochastic dynamics of lattice systems with finite local state space, possibly at
low temperature, and possibly non-reversible. We assume the additional regularity …