Claudio Giberti

Duality for stochastic models of transport

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process which is obtained by placing the system in contact with proper reservoirs, working at different particle densities or different temperatures. We show that all the models are exactly solvable by duality, using a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization limit in which particles or energy is instantaneously redistributed among sites.The results shows that duality is a versatile tool for analyzing stochastic models of transport, while the analysis in the literature has been so far limited to particular instances. Long-range correlations naturally emerge as a result of the interaction of dual particles at the microscopic level and the explicit computations of covariances match, in the scaling limit, the predictions of the macroscopic fluctuation theory.

Common periodic behavior in larger and larger truncations of the Navier-Stokes equations

The periodic behavior ofN-mode truncations of the Navier-Stokes equations on a two-dimensional torus is studied forN=44, 60, 80, and 98. Significant common features are found, particularly for not too high Reynolds numbers. In all models periodicity ends, giving rise, though at quite different parameter values, to quasiperiodicity.

Ultrametricity in the Edwards-Anderson Model

We test the property of ultrametricity for the spin-glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to 20(3) spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution, our result contradicts the droplet theory.

Behavior of a three-torus in truncated Navier-Stokes equations

Abstract The presence of a three-torus in a seven-mode truncation of the three-dimensional Navier—Stokes equations is investigated numerically by means of cross-section and power spectra. Furthermore, by taking advantage of particular features of the model, rotation vectors, circle maps and torus maps can be computed with high accuracy and used to study the dynamics. In particular, some interesting phenomena of partial phase-locking are described in deep detail. The three-torus, which arises via a Hopf bifurcation and persists in a wide parameter range, is found to break and originate a strange attractor. The onset of chaos and the associated bifurcation point can be defined quite precisely.

Quenched central limit theorems for the Ising model on random graphs

The main goal of the paper is to prove central limit theorems for the magnetization rescaled by

ON THE PRESENCE OF NORMALLY ATTRACTING MANIFOLDS CONTAINING PERIODIC OR QUASIPERIODIC ORBITS IN COUPLED MAP LATTICES

\sqrt{N}

Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs

N for the Ising model on random graphs with N vertices. Both random quenched and averaged quenched measures are considered. We work in the uniqueness regime