Group leader: Andrea Agazzi
Stochastic analysis deals with the study of systems evolving in time under the influence of randomness. We employ techniques from probability theory and statistical physics to analyze complex dynamical phenomena arising in diverse scientific fields. Our research is primarily concerned with systems of interacting particles, focusing on how simple, microscopic interactions translate into complex, macroscopic behaviors. We apply advanced stochastic analysis techniques to rigorously understand scaling limits and structural properties of such systems.
Specific areas of active research include:
- Mathematical foundations of machine learning algorithms, particularly deep neural networks.
- Stochastic dynamics of chemical reaction networks, with applications to system biology.
- Mean-field games applied to traffic flow management.
- Stochastic models in fluid dynamics.
Our group maintains active research collaborations with Federico Pasqualotto (UCSD), Jonathan Mattingly (Duke University), and the Probability Group at the University of Pisa.
