Punktprozesse mit Wechselwirkung |
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Authors: | Nguyen Xuan Xanh Hans Zessin |
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Institution: | (1) FakultÄt für Mathematik, UniversitÄtsstra\e, D-4800 Bielefeld 1, Bundesrepublik Deutschland |
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Abstract: | 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.
Danken möchten wir Klaus Krickeberg, der diese Arbeit durch eine Fülle wertvoller Hinweise und Anregungen gefördert hat. |
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