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 finite state Markov chains: a recursive procedure to identify slow variables for model reduction

Consider a sequence $(\eta^N(t) :t\ge 0)$ of continuous-time, irreducible Markov chains evolving on a fixed finite set $E$, indexed by a parameter $N$. Denote by $R_N(\eta,\xi)$ the jump rates of the Markov chain $\eta^N_t$, and assume that for any pair of bonds $(\eta,\xi)$, $(\eta',\xi')$ $\arctan \{R_N(\eta,\xi)/R_N(\eta',\xi')\}$ converges as $N\uparrow\infty$. Under a hypothesis slightly more restrictive (cf. \eqref{mhyp} below), we present a recursive procedure which provides a sequence of increasing time-scales \theta^1_N, \dots, \theta^{\mf p}_N, $\theta^j_N \ll \theta^{j+1}_N$, and of coarsening partitions \{\ms E^j_1, \dots, \ms E^j_{\mf n_j}, \Delta^j\}, 1\le j\le \mf p, of the set $E$. Let \phi_j: E \to \{0,1, \dots, \mf n_j\} be the projection defined by \phi_j(\eta) = \sum_{x=1}^{\mf n_j} x \, \mb 1\{\eta \in \ms E^j_x\}. For each 1\le j\le \mf p, we prove that the hidden Markov chain $X^j_N(t) = \phi_j(\eta^N(t\theta^j_N))$ converges to a Markov chain on \{1, \dots, \mf n_j\}