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.