My research interests mainly focus on Probability Theory, in particular I work on projects related to:
Central limit theorems for chaos expansions
Random polymers and disordered systems
Scaling limits and singular stochastic PDEs
Preprints
C. Cosco, F. Cottini and A. Donadini. The intermediate regime for two-dimensional directed polymers with critical spatial correlation. (to be posted on arXiv soon)
F. Caravenna, F. Cottini and G. Peccati. On irreducible central limit theorems. (to be posted on arXiv soon)
Publications
F. Caravenna, F. Cottini and M. Rossi. Quasi-critical fluctuations for 2d directed polymers. Ann. Appl. Probab. 35(4), 2604-2643, 2025. arXiv
F. Caravenna and F. Cottini. Gaussian Limits for Subcritical Chaos. Electron. J. Probab. 27, 1-35, 2022. arXiv
S. Bonaccorsi, F. Cottini and D. Mugnolo. Random evolution equations: well-posedness, asymptotics, and applications to graphs. Appl. Math. Optim. 84, 2849-2887, 2021. arXiv
Others
F. Cottini. Central limit theorems for polynomial chaos and fluctuations for 2d directed polymers. Ph.D. thesis, Università degli Studi di Milano-Bicocca, 2023. PDF
My collaborators
Stefano Bonaccorsi (Università degli Studi di Trento)
Francesco Caravenna (Università degli Studi di Milano-Bicocca)
Clément Cosco (Université Paris Dauphine)
Anna Donadini (Università degli Studi di Milano-Bicocca)
Delio Mugnolo (University of Hagen)
Giovanni Peccati (University of Luxembourg)
Maurizia Rossi (Università degli Studi di Milano-Bicocca)
Selected slides*
On (ir)reducible central limit theorems for homogenenous sums PDF
Gaussian limits for polynomial chaos and 2d directed polymers PDF
Gaussian fluctuations for 2d directed polymers in the quasi-critical regime PDF
Gaussian limits for subcritical chaos PDF
The Directed Polymer model: a "bridge" between Statistical Mechanics and Stochastic Analysis PDF
*all handwritten by me :)