Large interacting lattice systems: Gibbs states and phase transitions
Project goals
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. Ourpreceeding 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. Stationary states of conservative particle systems and the condensation in multiple-jump zero range processes for models of a traffic jam will be studied.The influence of the underlying lattice on interacting particle systems will be investigated. In particular, we will study survival of the contact process on the hierarchical group and on nonamenable lattices, the rebellious voter modelon "exotic" lattices, and we will analyse how the proof of phase transitions of lattice models with entropic barrier depends on the considered lattice.
Keywords
modely na mřížcefázové přechodyGibbsovy stavykontaktní procesykonzervativní částicový systém
Public support
Provider
Czech Science Foundation
Programme
Standard projects
Call for proposals
Standardní projekty 12 (SGA02009GA-ST)
Main participants
—
Contest type
VS - Public tender
Contract ID
201/09/1931
Alternative language
Project name in Czech
Velké interagující systémy na mřížce: Gibbsovy stavy a fázové přechody
Annotation in Czech
Zkoumání gradientních modelů s nekonvexním potenciálem včetně důkazu strikní konvexity volné energie. Analýza modelů s entropickou bariérou. Výběr modelu založený na pseudověrohodnosti. Sudium stacionárních stavů konservativních modelů. Přežívání hierarchických a neamenabilních kontaktních procesů.
Scientific branches
Completed project evaluation
Provider evaluation
U - Uspěl podle zadání (s publikovanými či patentovanými výsledky atd.)
Project results evaluation
The project gone according to plan both in terms of expertise and in terms of disbursement of funds.
Solution timeline
Realization period - beginning
Jan 1, 2009
Realization period - end
Dec 31, 2011
Project status
U - Finished project
Latest support payment
Apr 16, 2011
Data delivery to CEP
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data delivery code
CEP12-GA0-GA-U/02:2
Data delivery date
May 2, 2016
Finance
Total approved costs
2,605 thou. CZK
Public financial support
2,605 thou. CZK
Other public sources
0 thou. CZK
Non public and foreign sources
0 thou. CZK
Recognised costs
2 605 CZK thou.
Public support
2 605 CZK thou.
0%
Provider
Czech Science Foundation
CEP
BA - General mathematics
Solution period
01. 01. 2009 - 31. 12. 2011