Threshold phenomena in stochastic systems

Czech Science Foundation P201/12/2613

The project is devoted to a study of threshold phenomena: 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 the 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 proceses.

Principal investigator: Roman Kotecký
Associate investigator: Jan M. Swart (Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic)