We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In… (More)

We prove that the logarithmic-Sobolev constant for Zero-Range Processes in a box of diameter L may depend on L but not on the number of particles. This is a first, but relevant and quite technical… (More)

We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible… (More)

1 LATP, UMR 6632 du CNRS, Centre de Mathématique et Informatique, Université de Provence, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13, France. 2 Dipartimento di Matematica, Politecnico di Milano… (More)

Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses… (More)

We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the… (More)

The scalar di¤erential inclusion _ x A f ðxÞ þ gðxÞu; u A 1⁄2 1; 1 ; xð0Þ 1⁄4 x0 ð0:1Þ is considered as a model of the dynamical system _ x 1⁄4 f ðxÞ perturbed by the bounded noise gðxÞu, u A 1⁄2 1;… (More)