Punktprozesse mit Wechselwirkung

We consider classical, continuous systems of particles in r dimensions described by infinite system equilibrium states which have been defined by Dobrushin 5] and Lanford/Ruelle 24]. For a large class of potentials we prove the theorem of Lee/Yang 43] together with a variational characterizafor these equilibrium states. The main idea stems from Föllmer 9] who showed that in the case of lattice systems, the theorem of Lee/Yang is intimately related to Birkhoff's ergodic theorem and McMillan's theorem (ergodic theorem of information theory). Following this idea we obtain as main results an r-dimensional ergodic theorem for random measures in ^r , limit theorems concerning energy and entropy and an r-dimensional version of Breiman's theorem showing that there is almost sure convergence behind McMillan's theorem.

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Danken möchten wir Klaus Krickeberg, der diese Arbeit durch eine Fülle wertvoller Hinweise und Anregungen gefördert hat.