Institute of Information Theory and Automation

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Threshold phenomena in stochastic systems

Agency: 
GACR
Identification Code: 
GAP201/12/2613
Start: 
2012-01-01
End: 
2015-12-31
Project Focus: 
teoretický
Project Type (EU): 
other
Abstract: 
The project is devoted to the study of threshold phenomena: the abrupt and dramatic change in the properties of a stochastic system once a characteristic parameter passes a threshold value. General principles and various forms of threshold phenomena in large stochastic systems are analyzed. A number of concrete problems and conjectures is addressed concerning, in particular, gradient models and microscopic foundations of nonlinear elasticity, existence of entropically generated long-range order, stability in Kuramoto's model of dynamically coupled oscillators, transition to exponential growth of the contact process and rigorous upper bounds on the critical point of oriented percolation, existence of a noncoexisting phase in one-dimensional models of competing species, and the existence of product invariant laws and condensation for generalized zero-range processes.
Publications ÚTIA: 
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2015-01-06 14:03