Hydrodynamic limit of asymmetric exclusion processes under diffusive scaling in d≥3d\ge 3

We consider the asymmetric exclusion process. We start from a profile which is constant along the drift direction and prove that the density profile, under a diffusive rescaling of time, converges to the solution of a parabolic equation

Gaussian estimates for symmetric simple exclusion processes

We prove Gaussian tail estimates for the transition probability of $n$ particles evolving as symmetric exclusion processes on \bb Z^d, improving results obtained in \cite{l}. We derive from this result a non-equilibrium Boltzmann-Gibbs principle for the symmetric simple exclusion process in dimension 1 starting from a product measure with slowly varying parameter

Coupled dark energy: a dynamical analysis with complex scalar field

The dynamical analysis for coupled dark energy with dark matter is presented, where a complex scalar field is taken into account and it is considered in the presence of a barothropic fluid. We consider three dark energy candidates: quintessence, phantom and tachyon. The critical points are found and their stabilities analyzed, leading to the three cosmological eras (radiation, matter and dark energy), for a generic potential. The results presented here enlarge the previous analyses found in the literature.Comment: 9 pages, version accepted for publication in EPJC. arXiv admin note: text overlap with arXiv:1505.0324

Metastability of reversible finite state Markov processes

We prove the metastable behavior of reversible Markov processes on finite state spaces under minimal conditions on the jump rates. To illustrate the result we deduce the metastable behavior of the Ising model with a small magnetic field at very low temperature