Publications

Research Articles

1. 1. Brigati, Giovanni, Francis Lörler, and Lihan Wang. "Hypocoercivity meets lifts." Kinetic and Related Models (2026), online first, and arXiv preprint arXiv:2412.10890.

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

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

   4. 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.

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

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

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

   8. Brigati, Giovanni, 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).

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

Preprints

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

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

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

   13. Brigati, Giovanni, 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).

Proceedings, Book Chapters, and Special Issues

1. 14. Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. "From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties." arXiv preprint arXiv:2507.11387 (2025). (Accepted in a special issue of Mathematical Models and Methods in Applied Sciences).

   15. Brigati, Giovanni, Jean Dolbeault, and Nikita Simonov. "Logarithmic Sobolev inequalities: a review on stability and instability results." arXiv preprint arXiv:2504.08658 (2025). (Accepted in a special issue of La Matematica).

   16. Brigati, Giovanni. "Nonlinear Dirichlet forms, energy spaces, and calculus rules." arXiv preprint arXiv:2309.00377 (2023).

Other

1. 17. Brigati Giovanni, 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

Brigati, Giovanni . 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.