Abstract We prove the hydrodynamical limit for weakly asymmetric simple exclusion processes. A large deviation property with respect to this is established symmetric case. treat also situation where a slow reaction (creation and annihilation of particles) present.

Anomalous large thermal conductivity has been observed numerically and experimentally in one- two-dimensional systems. There is an open debate about the role of conservation momentum. We introduce a model whose diverges dimensions 1 2 if momentum conserved, while it remains finite dimension $d\ensuremath{\ge}3$. consider system harmonic oscillators perturbed by nonlinear stochastic dynamics conserving energy. compute explicitly time correlation function energy current ${C}_{J}(t)$, we find...

Consider a Markov chain $\{X_n\}_{n\ge 0}$ with an ergodic probability measure $π$. Let $Ψ$ function on the state space of chain, $α$-tails respect to $π$, $α\in (0,2)$. We find sufficient conditions transition prove convergence in law $N^{1/α}\sum_n^N Ψ(X_n)$ $α$-stable law. ``Martingale approximation'' approach and ``coupling'' give two different sets conditions. extend these results continuous time jump processes $X_t$, whose skeleton satisfies our assumptions. If waiting between jumps...

We study the large scale space–time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For strictly convex interaction potential we prove that on these are governed infinite-dimensional Ornstein –Uhlenbeck process. Its effective diffusion type covariance matrix characterized through variational formula.

For a system of weakly interacting anharmonic oscillators, perturbed by an energy-preserving stochastic dynamics, we prove autonomous (stochastic) evolution for the energies at large time scale (with respect to coupling parameter). It turns out that this macroscopic is given so-called conservative (nongradient) Ginzburg-Landau differential equations. The proof exploits hypocoercivity and hypoellipticity properties uncoupled dynamics.

We consider a one dimensional infinite chain of har- monic oscillators whose dynamics is perturbed by stochastic term conserving energy and momentum. prove that in the unpinned case macroscopic evolution converges to fractional diffusion. For pinned system we evolves diffusively, generalizing some results [4].

We prove the hydrodynamic limit for a one-dimensional harmonic chain of interacting atoms with random flip momentum sign. The system is open: at left boundary it attached to heat bath temperature $T_-$, while right endpoint subject an action force which reads as $\bar F + \frac 1{\sqrt n} \widetilde{\mathcal F} (n^2 t)$, where \ge0$ and $\widetilde{\mathcal F}(t)$ periodic function. Here $n$ size microscopic system. Under diffusive scaling space-time, we that empirical profiles two locally...

We consider chains of rotors subjected to both thermal and mechanical forcings in a nonequilibrium steady state. Unusual nonlinear profiles temperature velocities are observed the system. In particular, is maximal center, which an indication nonlocal behavior Despite this uncommon behavior, local equilibrium holds for long enough chains. Our numerical results also show that when forcing strong enough, energy current can be increased by inverse gradient. This counterintuitive result again...

Nous prouvons la relation d'Einstein pour certaines marches aléatoires biaisées sur des arbres de Galton–Watson. Cette formule relie dérivée vitesse à diffusivité l'équilibre. Ce travail fournit le premier exemple preuve une dynamique dans un milieu aléatoire qui comporte pièges arbitrairement lents.