ERGODICITY OF INFINITE HAMILTONIAN SYSTEMS WITH CONSERVATIVE NOISE

                    by
                    
Carlangelo  Liverani  (II Universita` di Roma)
                    
                    and
                    
Stefano Olla   (Politecnico di Torino, Italy, and CMAP, Ecole Polytechnique , Palaiseau France)




We study the stationary measures of an infinite Hamiltonian system of 
interacting particles in $\RR^3$ subject to a stochastic local perturbation
conserving energy and momentum. We prove that all the translation invariant
measures that are stationary for the deterministic Hamiltonian dynamics,
reversible for the stochastic dynamics, and that satisfy some regularity 
conditions are convex combination of ``Gibbs'' states. This result implies
hydrodynamical behavior for the systems under consideration.

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                ABSTRACT.liverani_olla_294