06-70 Fern ndez R.
Gibbsianness and non-Gibbsianness in lattice random fields (198K, LATeX 2e) Mar 15, 06
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Abstract. These are the notes for a minicourse at the Les Houches summer school \emph{Mathematical Statistical Physics} (July 4- July 29, 2005) The main topics of the course are the following: (i) Review, with some detail, of the topological and measure-theoretical notions needed to define Gibbs measures. (ii) The notion of specification and discussion of properties related to Gibbsianness (non-nullness, directional quasilocality, continuity\ldots) (iii) Kozlov's theorem relating Gibbsianness with non-nullness and quasilocality: (hopefully) pedagogical presentation of the proof and discussion of its consequences for weaker forms of Gibbsianness. (iv) Non-Gibbsianness of measures obtained via linear transformations: mechnisms and strategy of proofs. (v) Three benchmark examples of non-Gibbsianness: renormalization maps, spin-flip evolutions and disordered models.

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