Project leader: Doc. RNDr. Martin Janžura, CSc.

Department: SI

Supported by (ID): GA201/09/1931

Duration: 2009-2011

Details: here

Publications at UTIA: list

Abstract:

The aim of the project is to develop several aspects of the theory of Gibbs states and phase transitions of lattice models. Gradient lattice models, where the challenge is to understand the case of non-convex potentials, will be studied by means of multiscale analysis and a refinement of cluster expansions. In particular, we will present a proof of the strict convexity of the free energy and unicity of Gibbs states corresponding to a given tilt/deformation for a class of models at low temperatures.Our preceeding proof of coexistence of two distinct Gibbs states with the same tilt will be extended to a bigger class of nonconvex potentials. The results of the statistical analysis for Gibbs random fields as spatial models will be generalized to the corresponding spatio-temporal models. A model selection method based on the penalized pseudo-likelihood will be presented.