RESEARCH ACTIVITIES

My research interests focus maily on the applications of probability theory and of the theory of stochastic processes. In particular my attention is devoted to the connections between probability and mathematical physics, that is to equilibrium and non-equilibrium classical and quantum statistical mechanics, interacting particle systems and multy-agent dynamics, as well as to the asymptotic properties of dynamical systems.

• My current principal research efforts are devoted to the study of the exact asymptotics of finite connections for the Bernoulli bond percolation and for the Random Cluster models in the supercritical regime, as well as to extend the techniques developed to tackle this problem to the analysis of the exact asymptotics of (truncated) correlation functions for spin systems.
  On this research line I maily collaborate with Massimo Campanino.

• I am also interested in the study the behaviour of systems consisting of a large number of simple (in general identical) subsystems (agents), whose time evolution is subject to feedback control rules taking into account the dynamical state of the single agent and of its neighbours, but also the boundary conditions and random perturbations of the communication protocol. The main question concerning these models is if, varying the control parameters and the initial conditions, the system evolution attains particular dynamical states, which in the literature go by the name of flocking or swarming, as well as consensus, either when the size of the sistem is finite or in the limit of the number of agents tending to infinity (kinetic limit).
  On this research line I have maily collaborated with Enza Orlandi.