Lorenzo Bertini

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We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager–Machlup theory in the SNS; a general(More)
We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation j of the empirical current with a rate functional I(j). We then estimate the probability of a fluctuation of the(More)
The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non–equilibrium, namely for non reversible systems. In this paper we consider a simple example of a non–equilibrium situation, the symmetric simple exclusion process in which we let the system exchange particles with(More)
– We consider a continuous gas in a d-dimensional rectangular box with a finite range, positive pair potential, and we construct a Markov process in which particles appear and disappear with appropriate rates so that the process is reversible w.r.t. the Gibbs measure. If the thermodynamical paramenters are such that the Gibbs specification satisfies a(More)
1 Dipartimento di Matematica, Università di Roma La Sapienza P.le A. Moro 2, 00185 Roma, Italy E–mail: bertini@mat.uniroma1.it 2 Dipartimento di Matematica, Università di Roma La Sapienza, Roma, Italy Mathematics Department, Harvard University, Cambridge MA, USA E–mail: desole@mat.uniroma1.it 3 Dipartimento di Matematica, Università dell’Aquila 67100(More)
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a unified picture is emerging at the macroscopic level, applicable, in our view, to real phenomena where diffusion is the(More)
Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models and consider them in a finite volume of size l in contact with particle reservoirs at the boundary. We prove that, as(More)
The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own(More)