98-567 Fern\'andez R.

Measures for lattice systems (93K, LATeX 2e) Aug 18, 98

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Abstract. I review issues related with the presence or absence of Gibbsianness in measures describing random fields in lattices. After a brief exposition of the definition and properties of Gibbs measures, I discuss the phenomenon of non-Gibbsianness. The discussion involves three aspects: (1) Examples among renormalized measures and invariant measures of stochastic transformations; (2) probabilistic characterization of non-Gibbsian measures ---lack of quasilocality and ``wrong'' large-deviation properties---, and (3) proposed clasification schemes and notions of generalized Gibbsianness. The review closes with comments on directions for further work. [Contribution to the proceedings of Statphys 20]

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