On the dynamical behavior of the ABC model

We consider the ABC dynamics, with equal density of the three species, on the discrete ring with $N$ sites. In this case, the process is reversible with respect to a Gibbs measure with a mean field interaction that undergoes a second order phase transition. We analyze the relaxation time of the dynamics and show that at high temperature it grows at most as $N^2$ while it grows at least as $N^3$ at low temperature

Equilibrium fluctuations of additive functionals of zero-range models

For mean-zero and asymmetric zero-range processes on $\Z^d$, the fluctuations of additive functionals starting from an invariant measure are considered. Under certain assumptions, we establish when the fluctuations are diffusive and satisfy functional central limit theorems. These results complement those for symmetric zero-range systems and also those for simple exclusion models already in the literature.FC