Vedoucí projektu: Doc. RNDr. Martin Janžura, CSc.

Oddělení: SI

Podporováno (ID): GA201/06/1323

Trvání: 2006 - 2008

Abstrakt:

Phase transitions of complex systems are studied with help of probabilistic and analytic methods. The techniques of Pirogov-Sinai theory and cluster expansion are further developed and applied. The classes of investigated lattice models include Kac models with additional short-range interaction (including an application to random networks), phase transition of tilings, and models with continuum spins. Coexistence of phases is investigated. In particular, birth of an equilibrium droplet at the edge of phase coexistence region is discussed and new results concerning its asymptotic behaviour are proven. Gibbs random fields are applied as probability models for image processing with a special view on effects of phase coexistence. The problem of efficiency of estimates is investigated. Site disordered zero-range processes are studied in the hydrodynamic limit. Applications of interacting particle models in population biology are discussed.