In interacting stochastic models, simple rules on the local level can give rise to complex behaviour on large scales. A natural way to study this phenomenon is through scaling limits and examination of the corresponding asymptomatic behaviour. Sometimes, randomness is present even at the macroscopic level, motivating the study of random continuum models.
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.