Topics in Statistical Physics and Probability Theory
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چکیده
We discuss some basic facts regarding Gibbs measures on the infinite lattice Zd. Our discussion is restricted to an explicit case with nearest-neighbor interactions but the reader should note that the general theory allows much more flexibility; see Friedli and Velenik [3, Chapter 6] for additional details. Preliminaries. Let (S,S, λ) be a measure space (λ is a positive measure, either finite or infinite). We assume that S is a Polish space (metric, separable and complete) with S its Borel sigma algebra (this is convenient in order to define Gibbs measures through regular conditional probabilities as we do, though it is possible to develop the theory under weaker assumptions). Fix an integer d > 1. We will consider various probability measures on the measurable space
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تاریخ انتشار 2017