Email: gianfelice[AT]mat.unical.it; michele.gianfelice[AT]unical.it
Web: Personal site
Stochastic processes and random fields
My research interests belong maily to the domain of 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 statistical mechanics, interacting particle systems and multi-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 particular 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 classical compact spin systems.
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).
Furthermore, I am currently working on the stochastic stability of the Lorenz'63 flow under random perturbations modeling the anthropogenic forcing and I am also involved in the study the asympotic properties of certain flows arising from approximating the quasi-geostrophic models of the athmospheric evolution by means of an Hamiltonian reduction scheme. Our aim is to characterize the statistical properties of these flows, as well as its statistical and stochastic stability, extending the results previously obtained for the Lorenz'63 flow.
Teaching - Academic Year 2019/2020:
- PROBABILITA' E PROCESSI STOCASTICI (CdS Magistrale in Matematica)