Fern ndez R.
Gibbsianness and non-Gibbsianness in lattice random fields
(198K, LATeX 2e)
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.