"15"^^ . "15"^^ . . "http://www.isvav.cz/projectDetail.do?rowId=GA201/06/1323"^^ . . . . . . . "GA201/06/1323" . "Bylo dosa\u017Eeno nov\u00FDch v\u00FDsledk\u016F ve studiu gradientn\u00EDch model\u016F s nekonvexn\u00EDm potenci\u00E1lem. Byl zkonstruov\u00E1n prvn\u00ED p\u0159\u00EDklad f\u00E1zov\u00E9ho p\u0159echodu pro gradientn\u00ED model. Pro diskusi striktn\u00ED konvexity voln\u00E9 energie p\u0159i n\u00EDzk\u00FDch teplot\u00E1ch jsou aplikov\u00E1ny techniky vych"@cs . . " lattice models" . . "2009-10-22+02:00"^^ . "Pravd\u011Bpodobnostn\u00ED metody ve studiu f\u00E1zov\u00FDch p\u0159echod\u016F komplexn\u00EDch syst\u00E9m\u016F" . "2006-01-01+01:00"^^ . "phase transitions; Gibbs states; lattice models; interacting particle systems; Pirogov-Sinai theory"@en . "2008-04-25+02:00"^^ . "Probabilistic methods in the study of phase transitions of complex systems"@en . . "phase transitions" . "1"^^ . . . " interacting particle systems" . . "F\u00E1zov\u00E9 p\u0159echody jsou studov\u00E1ny s pomoc\u00ED pravd\u011Bpodobnostn\u00EDch a analytick\u00FDch metod. Jsou d\u00E1le rozv\u00EDjeny a aplikov\u00E1ny techniky Pirogov-Sinajovy teorie a klastrov\u00FDch rozvoj\u016F. T\u0159\u00EDdy studovan\u00FDch m\u0159\u00ED\u017Ekov\u00FDch model\u016F zahrnuj\u00ED Kac\u016Fv model s dodate\u010Dnou kr\u00E1tce-dosahovou interakc\u00ED (v\u010Detn\u011B aplikace na n\u00E1hodn\u00E9 s\u00EDt\u011B), f\u00E1zov\u00E9 p\u0159echody syst\u00E9m\u016F pokr\u00FDv\u00E1n\u00ED, modely se spojit\u00FDm spinem. Je studov\u00E1na koexistence f\u00E1z\u00ED. Zvl\u00E1\u0161t\u011B je diskutov\u00E1n vznik kapky na hranici koexistence f\u00E1z\u00ED a jsou odvozov\u00E1ny nov\u00E9 v\u00FDsledky t\u00FDkaj\u00EDc\u00ED se p\u0159\u00EDslu\u0161n\u00E9ho asymptotick\u00E9ho chov\u00E1n\u00ED. Gibbsova n\u00E1hodn\u00E1 pole jsou aplikov\u00E1na jako pravd\u011Bpodobnostn\u00ED modely pro zpracov\u00E1n\u00ED obraz\u016F se speci\u00E1ln\u00EDm p\u0159ihl\u00E9dnut\u00EDm na efekty f\u00E1zov\u00E9 koexistence. Je zkoum\u00E1n probl\u00E9m \u00FA\u010Dinnosti odhad\u016F. Jsou studov\u00E1ny bodov\u011B neuspo\u0159\u00E1dan\u00E9 procesy nulov\u00E9ho dosahu v hydrodynamick\u00E9 limit\u011B. T\u00E9\u017E jsou diskutov\u00E1ny aplikace model\u016F interaguj\u00EDc\u00EDch \u010D\u00E1stic v popula\u010Dn\u00ED biologii." . "1"^^ . . " Gibbs states" . "2008-12-31+01:00"^^ . "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."@en . "New results were obtained in the study of gradient models with a non-convex potential. A first example of a phase transition for a gradient model has been constructed. For a discussion of the strict convexity of the free energy at low temperatures, techn"@en . . "0"^^ . . . . .