One-dimensional random field Kac's model: localization of the phases

We study the typical profiles of a one dimensional random field Kac model, for values of the temperature and magnitude of the field in the region of the two absolute minima for the free energy of the corresponding random field Curie Weiss model. We show that, for a set of realizations of the random field of overwhelming probability, the localization of the two phases corresponding to the previous minima is completely determined. Namely, we are able to construct random intervals tagged with a sign, where typically, with respect to the infinite volume Gibbs measure, the profile is rigid and takes, according to the sign, one of the two values corresponding to the previous minima. Moreover, we characterize the transition from one phase to the other

Truncated correlations in the stirring process with births and deaths

We consider the stirring process in the interval \La_N:=[-N,N] of $\mathbb Z$ with births and deaths taking place in the intervals $I_+:=(N-K,N]$, $K>0$, and respectively $I_-:=[-N,-N+K)$. We prove bounds on the truncated moments uniform in $N$ which yield strong factorization properties

Spectral gap in stationary non-equilibrium processes

In this paper we study the spectral gap for a family of interacting particles systems on $[-N,N]$, proving that it is of the order $N^{-2}$. The system arises as a natural model for current reservoirs and Fick's law

Exponential rate of convergence in current reservoirs

In this paper we consider a family of interacting particle systems on [−N, N] that arises as a natural model for current reservoirs and Fick’s law. We study the exponential rate of convergence to the stationary measure, which we prove to be of the order N−2