Research Articles

1. 1. Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. "From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties." Mathematical Models and Methods in Applied Sciences (2026), 36 (06), 1185–1233.

   2. Giovanni Brigati, Jean Dolbeault, and Nikita Simonov. "Logarithmic Sobolev inequalities: a review on stability and instability results." La Matematica (2026). Volume 5, article 5.

   3. Giovanni Brigati. "Nonlinear Dirichlet forms, energy spaces, and calculus rules." arXiv preprint arXiv:2309.00377 (2023). Accepted in La Matematica (2026).

   4. Giovanni Brigati, Francis Lörler, and Lihan Wang. "Hypocoercivity meets lifts." Kinetic and Related Models (2026).

   5. Giovanni Brigati, and Gabriel Stoltz. "How to Construct Explicit Decay Rates for Kinetic Fokker–Planck Equations?." SIAM Journal on Mathematical Analysis 57.4 (2025): 3587-3622.

   6. Giovanni Brigati, and Francesco Pedrotti. "Heat flow, log-concavity, and Lipschitz transport maps." Electronic Communications in Probability 30 (2025): 1-12.

   7. Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. "Multivariate Gini-type discrepancies." Mathematical Models and Methods in Applied Sciences (2025), 35(05), 1267-1296.

   8. Giovanni Brigati, Jean Dolbeault, and Nikita Simonov. "Stability for the logarithmic Sobolev inequality." Journal of Functional Analysis (2024): 110562.

   9. Giovanni Brigati, and Ivailo Hartarsky. "The normal contraction property for non-bilinear Dirichlet forms." Potential Analysis 60.1 (2024): 473-488.

   10. Giovanni Brigati, Jean Dolbeault, and Nikita Simonov. "On Gaussian interpolation inequalities." Comptes Rendus. Mathématique 362.G1 (2024): 21-44.

   11. Giovanni Brigati, Jean Dolbeault, and Nikita Simonov. "Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results." Annales de l'Institut Henri Poincaré C, Analyse non linéaire. (2023).

   12. Giovanni Brigati. "Time averages for kinetic Fokker-Planck equations." Kinetic and Related Models 16.4 (2023): 524-539.

   13. Giovanni Brigati, Gabriel Stoltz, Andi Qi Wang, and Lihan Wang. "Explicit convergence rates of underdamped Langevin dynamics under weighted and weak Poincar\'e--Lions inequalities." arXiv preprint arXiv:2407.16033 (2024). Accepted in Annals of Applied Probability

Preprints

1. 14. Giovanni Brigati, Guillaume Carlier, Jean Dolbeault, and Filippo Quattrocchi. "Nonlinear kinetic Fokker–Planck equations as gradient

flows of the free energy". preprint (2026) 

1. 15. Giovanni Brigati, Guillaume Carlier, and Jean Dolbeault, "The fundamental solution of a nonlinear kinetic Fokker--Planck equation". preprint arXiv:2603.26650 (2026).

   16. Giovanni Brigati, and Clément Mouhot. "Introduction to quantitative De Giorgi methods." preprint arXiv:2510.11481 (2025). (Lecture notes)

   17. Giovanni Brigati, and Lorenzo Dello Schiavo. "Non-bilinear Dirichlet Functionals: Markovianity, locality, invariance." arXiv preprint arXiv:2510.02942 (2025).

   18. Giovanni Brigati, Jan Maas, and Filippo Quattrocchi. "Kinetic Optimal Transport (OTIKIN)--Part 1: Second-Order Discrepancies Between Probability Measures." arXiv preprint arXiv:2502.15665 (2025).

Other

1. 19. Giovanni Brigati, Jean Dolbeault, Nikita Simonov. "Corrigendum to “Logarithmic Sobolev and interpolation inequalities on the sphere: Constructive stability results”. Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 2024.

PhD Thesis

Giovanni Brigati.  "Kinetic equations, functional inequalities, and distances in the space of probability measures". Université Paris sciences et lettres; Università degli studi (Pavie, Italie); Università degli studi di Milano - Bicocca; Istituto nazionale di alta matematica Francesco Severi (Italie (Rome)); Università degli Studi di Firenze, 2023. English.