Preprints on arXiv

Prépublications sur HAL

Publications on MathSciNet (subscription required)

Ph.D. in mathematics ENS Lyon 2001-2004 (includes papers [A1]-…-[A9]).

Habilitation Université Paris 6 2010, soon available (reviews papers [A10]-..-[A20] and [A23])

Titles link to the preprint when available.

Papers

• Introduction to quantitative De Giorgi methods (with G. Brigati) – Preprint 2025.
• Critical trajectories in kinetic geometry (with H. Dietert, L. Niebel and R. Zacher) – Preprint 2025.
• Half-space decay for linear kinetic equations (with E. Bouin and S. Mischler) – Preprint 2025.
• A consistency-stability approach to scaling limits of zero-range processes (with D. Marahrens and A. Menegaki) – Preprint 2024.
• Quantitative fluid approximation in fractional regimes of transport equations with more invariants (with É. Bouin and L. Kanzler) – Preprint 2024.
• Gehring’s Lemma for kinetic Fokker-Planck equations (with C. Imbert, J.Guerand) – Preprint 2024.
• Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators (with F. Anceschi, H. Dietert, J. Guerand, A. Loher and A. Rebucci) – Preprint 2024.
• Quantitative Geometric Control in Linear Kinetic Theory (with H. Dietert, F. Hérau and H. Hutridurga) – Preprint 2023.
• Control of Instability in a Vlasov-Poisson System Through an External Electric Field (with L. Einkemmer, Q. Li and Y. Yue) – J. Comput. Phys. 530 (2025), Paper No. 113904.
• Concentration in an advection-diffusion model with diffusion coefficient depending on the past trajectory (with C. Burtea and N. Meunier) – Discrete Contin. Dyn. Syst. 44 (2024), no. 12, 3649–3668.
• A consistence-stability approach to hydrodynamic limit of interacting particle systems on lattices (with A. Menegaki) – Séminaire Laurent Schwartz—Équations aux dérivées partielles et applications. Année 2021–2022, Exp. No. VII (15 pages)
• Trajectorial hypocoercivity and application to control theory (with H. Dietert, F. Hérau and H. Hutridurga) – Séminaire Laurent Schwartz—Équations aux dérivées partielles et applications. Année 2021–2022, Exp. No. VIII (10 pages)
• Special macroscopic modes and hypocoercivity (with K. Carrapatoso, J. Dolbeault, F. Hérau, S. Mischler and C. Schmeiser) – Preprint (62 pages) to appear in J. of the European Math. Society
• Quantitative De Giorgi methods in kinetic theory (with J. Guerand) – J. Éc. polytech. Math. 9 (2022), 1159–1181.
• Weighted Korn and Poincaré-Korn inequalities in the Euclidean space and associated operators (with K. Carrapatoso, J. Dolbeault, F. Hérau, S. Mischler) – Arch. Ration. Mech. Anal. 243 (2022), no. 3, 1565-1596.
• Quantitative fluid approximation in transport theory: a unified approach (with E. Bouin) – Probab. Math. Phys. 3 (2022), no. 3, 491–542.
• Linearized wave-damping structure of Vlasov-Poisson in (with J. Bedrossian and N. Masmoudi) – SIAM J. Math. Anal. 54 (2022), no. 4, 4379–4406.
• Gaussian lower bounds for the Boltzmann equation without cut-off (with C. Imbert and L. Silvestre) – SIAM Journal of Mathematical Analysis 52 (2020), no. 3, 2930-2944
• The Schauder estimate in kinetic theory with application to a toy nonlinear model (with C. Imbert) — Ann. H. Lebesgue 4 (2021), 369-405.
• Existence of self-accelerating fronts for a non-local reaction-diffusion equations (with N. Berestycki and G. Raoul) – Preprint (36 pages)
• Decay estimates for large velocities for the Boltzmann equation without cut-off (with C. Imbert and L. Silvestre) – Journal de l’École polytechnique – Mathématiques 7 (2020), 143-184
• Long time behavior in locally activated random walks (with N. Meunier and R. Roux) – Communications in Mathematical Sciences 17 (2019), no. 4, 1071-1094
• Hypocoercivity without confinement (with E. Bouin, J. Dolbeault, S. Mischler, C. Schmeiser) – Pure and Applied Analysis 2 (2020), no. 2, 203-232
• Uniqueness of the non-equilibrium steady state for a 1D BGK model in kinetic theory (with E. Carlen, L. Esposito, J. Lebowitz and R. Marra) – Acta Applicandae Mathematicae 169 (2020), 99-124
• De Giorgi-Nash-Moser and Hörmander theories: new interplay – Proceedings of the ICM 2018 (20 pages)
• From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight (with M. Briant and S. Merino) – Analysis and Applications 17 (2019), no. 1, 85-116.
• Factorization for non-symmetric operators and exponential H-theorem (with M. P. Gualdani and S. Mischler) – Mémoire de la Société Mathématique de France 153 (2017) (137 pages)
• Landau damping in finite regularity for unconfined systems with screened interactions (with J. Bedrossian and N. Masmoudi) Communications on Pure and Applied Mathematics 71 (2018), no 3, 537-576
• Approach to the steady state in kinetic models with thermal reservoirs at different temperatures – Journal of Statistical Physics 172 (2018), no. 2, 522-543
• Exponential decay to equilibrium for a fibre lay-down process on a moving conveyor belt (with E. Bouin and F. Hoffmann) – SIAM Journal on Mathematical Analysis (2017) 49(4), 3233–3251
• Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (with C. Imbert, F. Golse and A. Vasseur) – Annali della Scuola Normale Superiore di Pisa 5) 19 (2019), no. 1, 253-295 [Supersedes this previous preprint]
• Landau damping: paraproducts and Gevrey regularity (with J. Bedrossian and N. Masmoudi) – Annals of PDEs (2016), no. 1, Art. 4, 71 pp
• Exponential stability of slowly decaying solutions to the kinetic Fokker-Planck equation (with S. Mischler) – Archive for Rational Mechanics and Analysis (2016),Volume 221, Issue 2, pp 677–723
• Hypocoercivity for a linearized multi-species Boltzmann system (with E. S. Daus, A. Jüngel, N. Zamponi) – SIAM Journal of Mathematical Analysis (2016), Volume 48, Issue 1, pp 538–568
• On the Mean Field and Classical Limits of Quantum Mechanics (with F. Golse and T. Paul) – Communications in Mathematical Physics (2016),Volume 343, Issue 1, pp 165–205
• Towards an H-theorem for granular gases (with M. I. García de Soria, P. Maynar, S. Mischler, T. Rey, E. Trizac) – Journal of Statistical Mechanics: theory and experiments (2015), Volume 2015
• Exponential approach to, and properties of, a non-equilibrium steady state in a dilute gas (with E. Carlen and J. Lebowitz) – Braz. J. Probab. Stat. 29 (2015), no. 2, 372–386
• Kinetic Theory (with C. Villani) – Princeton Companion to Applied Mathematics (32 pages)
• On measure solutions to the Boltzmann equation, Part II: Rate of convergence to equilibrium (with X. Lu) – Journal of Differential Equations (2015), Volume 258, Issue 11, pp. 3742–3810
• Lyapunov functionals for boundary-driven nonlinear drift-diffusion processes (with T. Bodineau, J. Lebowitz, C. Villani) – Nonlinearity 27 (2014), pages 2111–2132
• Empirical measures and Vlasov hierarchies (with F. Golse and V. Ricci) – Kinetic Theory and Related Fields 6 (2013), pages 919 – 943
• A new approach to quantitative propagation of chaos for drift, diffusion and jump processes (with S. Mischler and B. Wennberg) – Probability Theory and Related Fields (2015), Volume 161, 1-2, pp 1-59
• Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation (with L. Pareschi and T. Rey) – Mathematical Modelling and Numerical Analysis 47 (2013), pages 1515-1531
• Kac’s Program in Kinetic Theory (with S. Mischler) – Inventiones mathematicae 193 (2013), pages 1-147 [Supersedes this previous preprint]
• Stabilité orbitale pour le système de Vlasov-Poisson gravitationnel, d’après Lemou-Méhats-Raphaël, Guo, Lin, Rein et al. – Séminaire Bourbaki, année 2011/2012, exposés 1043–1058 Astérisque No. 352 (2013), Exp. No. 1044 (49 pages)
• Exponential rate of convergence to equilibrium for a model describing fiber lay-down processes (with J. Dolbeault, A. Klar, C. Schmeiser) – Applied Mathematics Research eXpress (Vol. 2013), pages 165-175
• A new approach to the creation and propagation of exponential moments in the Boltzmann equation (with R. Alonso, J. Cañizo, I. Gamba) – Comm. Part. Diff. Equations 38 (2013), Issue 1, pages 155-169
• The Wigner-Fokker-Planck equation: Stationary states and large time behavior (with A. Arnold, I. Gamba, M. Gualdani, S. Mischler and C. Sparber) – Math. Models Meth. in Applied Science 22, 1250034 (2012) (31 pages)
• Les équations de l’irréversibilité Popularisation article in Dossier Pour La Science 74, january 2012
• On Measure Solutions of the Boltzmann Equation part I: Moment Production and Stability Estimates (with X. Lu) – Journal of Differential Equations 252 (2012), 3305-3363
• About Kac’s Program in Kinetic Theory (with S. Mischler) – C. R. Acad. Sci. Paris (2011),  Ser. I vol. 349, pp 1245-1250
• Stabilité non-linéaire pour l’équation de Vlasov-Poisson et amortissement Landau – Gazette des Mathématiques 130 (2011), pp 7-18
• Enlarging the functional space of decay estimates on semigroups – Progress in Analysis and its Applications (2010), Proceedings of the 7th International ISAAC Congress
• Hypocoercivity for linear kinetic equations conserving mass (with J. Dolbeault and C. Schmeiser) – Trans. Amer. Math. Soc. 367 (2015), 3807-3828
• On Landau damping (with C. Villani) – Acta Mathematica 207 (september 2011), 29-201
• Les surprenantes propriétés des plasmas… – Popularisation article published on the french website Images des mathématiques.
• Celebrating Cercignani’s conjecture for the Boltzmann equation (with L. Desvillettes and C. Villani) – Kinet. Relat. Models 4 (2011), pp 277-294
• Fractional Poincaré inequalities for general measures (with E. Russ & Y. Sire) – J. Math. Pures Appl. 95 (2011), pp 72-84
• Fractional diffusion limit for collisional kinetic equations (with A. Mellet and S. Mischler) – Arch. Rational Mech. Anal. 199 (2011), pp 493-525
• Analysis of spectral methods for the homogeneous Boltzmann equation (with F. Filbet) – Trans. Amer. Math. Soc. 363 (2011), pp 1947-1980
• Pourquoi les plasmas sont stables ? La Recherche 448, janvier 2011.
• Cédric Villani reçoit la médaille Fields – Gazette des Mathématiques 126 (2010), pp 85-87
• Landau damping (with C. Villani) [see also the french version Amortissement Landau] – J. Math. Phys. (2010), vol. 51, 015204 (10 pages)
• Rate of convergence to self-similarity for Smoluchowski’s coagulation equation with constant coefficients (with J.A. Cañizo and S. Mischler) – SIAM J. Math. Anal. (2010), vol. 41, pp 2283-2314
• Prix Henri Poincaré : Cédric Villani Matapli (2009), vol. 90, 49-60.
• Hypocoercivity for kinetic equations with linear relaxation terms (with J. Dolbeault and C. Schmeiser) – C. R. Acad. Sci. Paris (2009), Ser. I vol. 347, pp. 511-516
• On the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularity (with N. Fournier) – Comm. Math. Phys. (2009), vol. 289, pp 803-824
• Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited inelastic hard spheres (with S. Mischler) – Discrete and Cont. Dyn. Syst. – Series A (2009), vol. 24, pp 159-185
• Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres (with S. Mischler) – Comm. Math. Phys. (2009), vol. 288, pp 431-502
• Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions (with L. Desvillettes) – Arch. Rational Mech. Anal. (2009), vol. 193, pp 227-253
• Quelques résultats d’hypocoercitivité en théorie cinétique collisionnelle – Séminaire ÉDPs. 2007–2008, Exp. No. XVI, 21 pp., École Polytech., Palaiseau, (2009)
• Relaxation rate, diffusion approximation and Fick’s law for inelastic scattering Boltzmann models (with B. Lods and G. Toscani) – Kinetic and Related Models (2008), vol. 1, pp 223-248
• Large time behavior for the a priori bounds for the solutions to the spatially homogeneous Boltzmann equation with soft potentials (with L. Desvillettes) – Asymptotic Analysis (2007), vol. 54, pp 235-245
• Spectral gap and coercivity estimates for the linearized Boltzmann collision operator without angular cutoff (with R. Strain) – J. Maths Pures Appl. (2007), vol. 87, pp 515-535
• Quantitative linearized study of the Boltzmann collision operator and applications – Comm. Math. Sci. (2007), vol. 5, pp 73-86
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus (with L. Neumann) – Nonlinearity (2006), vol. 19, pp 969-998
• Solving the Boltzmann equation in (with F. Filbet and L. Pareschi) – SIAM J. Sci. Comput. (2006), vol. 28, pp 1029-1053
• Explicit coercivity estimates for the linearized Boltzmann and Landau operators – Comm. Part. Diff. Equations (2006), vol. 31, pp 1321-1348
• Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials – Comm. Math. Phys. (2006), vol. 261, pp 629-672
• Fast algorithms for computing the Boltzmann collision operator (with L. Pareschi) – Math. Comp. (2006), vol. 75, pp 1833-1852
• Cooling process for inelastic Boltzmann equations for hard spheres, Part II: Self-similar solutions and tail behavior (with S. Mischler) – J. Statist. Phys. (2006), vol. 124, pp 703-746
• Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem (with S. Mischler and M. R. Ricard) – J. Statist. Phys. (2006), vol. 124, pp 655-702
• Quantitative lower bound for the full Boltzmann equation, Part I: Periodic boundary conditions – Comm. Part. Diff. Equations (2005), vol. 30, pp 881-917
• About estimates for the spatially homogeneous Boltzmann equation (with L. Desvillettes) – Ann. I.H.P. An. non linéaire (2005), vol. 22, pp 127-142
• Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials (with C. Baranger) – Rev. Matem. Iberoam. (2005), vol. 21, pp 819-841
• Regularity theory for the spatially homogeneous Boltzmann equation with cut-off (with C. Villani) – Arch. Rational Mech. Anal. (2004), vol. 173, pp 169-212
• Fast methods for the Boltzmann collision integral (with L. Pareschi) – C. R. Acad. Sci. Paris (2004), Ser. I vol. 339, pp 71-76

Thèse – PhD thesis

Étude mathématique de quelques équations cinétiques collisionnelles (Mathematical study of some collisional kinetic equations).
PDF, PS, PDF short version (toc + introduction + bibliography), PS short version. Available also on the CNRS server TEL.
Thèse de doctorat effectuée sous la direction de C. Villani, soutenue en novembre 2004 (460 pages).
PhD thesis, supervisor C. Villani, defended in november 2004 (460 pages).

Miscalleneous

[a] Résolution d’équations différentielles par des méthodes de tir, rapport de stage de licence (RapportJussieu1999), effectué en juin-juillet 1999 à l’Université Paris 6 sous la direction de François Hamel (13 pages)

[b] Introduction to the Wigner Distribution and the high frequency approximation for hyperbolic systems (RapportStanford2000), rapport de stage de maîtrise, effectué en juillet-août 2000 à Stanford sous la direction de G. Papanicolaou (30 pages)

[c] Une nouvelle preuve de la propagation de la régularité pour l’équation de Boltzmann homogène avec cut-off et potentiels durs, rapport de stage de DEA, soutenu en septembre 2001 (37 pages), voir article [A1]