Stochastic models and their applications

The research group works at the interface between Probability Theory and Statistical Physics.

The focus is on the rigorous mathematical description of complex systems by adopting a probabilistic approach relying on the theory of both stochastic processes (e.g. dual processes) and equilibrium statistical mechanics (e.g. mean field models). The systems of interest are often models of elementary constituents (particles) of physical systems. This is complemented with an interpretation of systems as models of individuals in a large population.

Three levels of description are often considered in the analysis:

  • the average behavior, as described by law of large numbers and concentration of measures
  • the typical fluctuations, and the identification of different universality classes (gaussian, KPZ and beyond)
  • the large deviations, including the estimate of small probabilities of rare events.

The numerical approach both stochastic and deterministic is also used to study problems that are out of reach of the analytical treatment.

A list of specific fields of expertise includes:

Stochastic processes

  • Probabilistic models
  • Interacting particle systems
  • Random networks/graphs
  • Large deviations and rare events
  • Applications to epidemics in population dynamics, transport models, population dynamics

Statistical mechanics

  • Complex system models
  • Disordered network models
  • Inverse problems
  • Molecular dynamical models
  • Applications to statistical inference, medicine, social and economic sciences

Staff researchers: Cristian Giardiną, Claudio Giberti, Gioia Carinci, Marco Maioli, Francesco Unguendoli, Cecilia Vernia.