Zur topologischen Beschreibung stochastischer Felder mit verallgemeinerten Spezifikationen

Abstract

Considering generalized specifications of stochastic fields on an arbitrary Polish space$(\Omega ,\tau ,\underline{\underline F} )$ as proposed in [Föllmer “Phase Transition and Martin Boundary”, Lect. Not. Math. 465 (1975)] this article deals with the topological description of the set of all specified stochastic fields as a Choquetsimplex which is a well known result in the frame of specifications on the n-dimensional lattice, as usually treated in Statistical Mechanics. However, in our situation the underlying space$(\Omega ,\underline{\underline F} _v )$ where$\underline{\underline F} _v$ is a subfield of$\underline{\underline F}$ does not permit a nice topological description. Based on results of generating the field$\underline{\underline F} _v$ by means of the specification itself we, therefore, introduce a properly chosen equivalence relation which leads to separated topological spaces. This yields the desired description as a direct generalization of the above mentioned results.