Threshold phenomena in stochastic systems

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.