Seminari del Dipartimento

Probabilita'

I will discuss the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular I will discuss two different discrete geometric constructions. Both of them are applied to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions it is possible to generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in
a gradient part, a circulation term and an harmonic component. All the three components are associated to functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and I will use this decomposition to construct models having a fixed invariant measure. Joint work with L. De Carlo
org: SCOPPOLA Elisabetta