ON THE CONNECTION BETWEEN A SOLUTION OF THE BOLTZMANN EQUATION AND A SOLUTION OF THE LANDAU-FOKKER-PLANCK EQUATION, Mathematics of the USSR-Sbornik, vol.69, issue.2, pp.465-478, 1991. ,
DOI : 10.1070/SM1991v069n02ABEH001244
Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials, Revista Matem??tica Iberoamericana, vol.21, pp.819-841, 2005. ,
DOI : 10.4171/RMI/436
URL : https://hal.archives-ouvertes.fr/hal-00087219
Entropy of spherical marginals and related inequalities, Journal de Math??matiques Pures et Appliqu??es, vol.86, issue.2, pp.89-99, 2006. ,
DOI : 10.1016/j.matpur.2006.04.003
URL : https://hal.archives-ouvertes.fr/hal-00693099
Survey on probabilistic methods for the study of the Kac-like equations, Boll. Unoone Mat .Ital, vol.4, issue.2, pp.187-212, 2011. ,
Central limit theorem for a class of one-dimensional kinetic equations, Probability Theory and Related Fields, vol.47, issue.1, pp.1-2, 2011. ,
DOI : 10.1007/s00440-010-0269-8
Increasing propagation of chaos for mean field models, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.35, issue.1, pp.85-102, 1999. ,
DOI : 10.1016/S0246-0203(99)80006-5
The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules, Mathematical physics reviews, pp.111-233, 1988. ,
From particle systems to the Landau equation : a consistency result ,
Weitere studien über das wärmegleichgewicht unter gasmolekülen Translation : Further studies on the thermal equilibrium of gas molecules, Sitzungsberichte der Akademie der Wissenschaften Kinetic Theory, pp.275-370, 1872. ,
The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles, Communications in Mathematical Physics, vol.35, issue.2, pp.101-113, 1977. ,
DOI : 10.1007/BF01611497
Superadditivity of Fisher's information and logarithmic Sobolev inequalities, Journal of Functional Analysis, vol.101, issue.1, pp.194-211, 1991. ,
DOI : 10.1016/0022-1236(91)90155-X
Entropy and chaos in the Kac model, Kinetic and Related Models, vol.3, issue.1, pp.85-122, 2010. ,
DOI : 10.3934/krm.2010.3.85
Many-body aspects of approach to equilibrium, Séminaire Equations aux Dérivées Partielles Exp. No. XI, 12 pp., Univ. Nantes, 2000. ,
DOI : 10.5802/jedp.575
Determination of the spectral gap for Kac's master equation and related stochastic evolution, Acta Mathematica, vol.191, issue.1, pp.1-54, 2003. ,
DOI : 10.1007/BF02392695
Determination of the Spectral Gap in the Kac Model for Physical Momentum and Energy-Conserving Collisions, SIAM Journal on Mathematical Analysis, vol.40, issue.1 ,
DOI : 10.1137/070695423
A sharp analog of Young???s inequality on SN and related entropy inequalities, Journal of Geometric Analysis, vol.102, issue.2, pp.3-487, 2004. ,
DOI : 10.1007/BF02922101
Exponential convergence to equilibrium for the homogeneous Landau equation ,
URL : https://hal.archives-ouvertes.fr/hal-00851757
Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules, Kinetic and Related Models, vol.9, issue.1 ,
DOI : 10.3934/krm.2016.9.1
URL : https://hal.archives-ouvertes.fr/hal-00765621
Quantitative and qualitative Kac???s chaos on the Boltzmann???s sphere, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.51, issue.3 ,
DOI : 10.1214/14-AIHP612
Chaos and entropic chaos for Kac's model without hig moments, Electron. J. Probab, vol.18, pp.78-79, 2013. ,
H-Theorem and trend to equilibrium in the kinetic theory of gases, Arch. Mech. (Arch. Mech. Stos.), vol.34, issue.3, pp.231-241, 1983. ,
The Boltzmann equation and its applications, 1988. ,
DOI : 10.1007/978-1-4612-1039-9
The Mathematical Theory of Non-Uniform Gases, American Journal of Physics, vol.30, issue.5, 1952. ,
DOI : 10.1119/1.1942035
Dispersion Relations for the Linearized Fokker-Planck Equation, Archive for Rational Mechanics and Analysis, vol.138, issue.2, pp.137-167, 1997. ,
DOI : 10.1007/s002050050038
THE FOKKER-PLANCK ASYMPTOTICS OF THE BOLTZMANN COLLISION OPERATOR IN THE COULOMB CASE, Mathematical Models and Methods in Applied Sciences, vol.02, issue.02, pp.167-182, 1992. ,
DOI : 10.1142/S0218202592000119
On asymptotics of the Boltzmann equation when the collisions become grazing, Transport Theory and Statistical Physics, vol.3, issue.3, pp.259-276, 1992. ,
DOI : 10.1007/BF00264463
Celebrating Cercignani's conjecture for the Boltzmann equation, Kinet. Relat. Models, vol.4, issue.1, pp.277-294, 2011. ,
On the spatially homogeneous landau equation for hard potentials part i : existence, uniqueness and smoothness, Communications in Partial Differential Equations, vol.1, issue.1-2, pp.1-2, 2000. ,
DOI : 10.1007/BF02183613
On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications, Communications in Partial Differential Equations, vol.315, issue.1-2, pp.1-2, 2000. ,
DOI : 10.1007/s002050050106
A dozen de Finetti-style results in search of a theory, Ann. Inst. H. Poincaré Probab. Statist, vol.23, issue.2, pp.397-423, 1987. ,
Vlasov equations, Functional Analysis and Its Applications, vol.5, issue.3, pp.48-58, 1979. ,
DOI : 10.1007/BF01077243
Reaching the best possible rate of convergence to equilibrium for solutions of Kac???s equation via central limit theorem, The Annals of Applied Probability, vol.19, issue.1, pp.186-209, 2009. ,
DOI : 10.1214/08-AAP538
A few ways to destroy entropic chaoticity on Kac's sphere. To appear in Comm, Math. Sci ,
On Villani's conjecture concerning entropy production for the Kac Master equation, Kinetic and Related Models, vol.4, issue.2, pp.479-497, 2011. ,
DOI : 10.3934/krm.2011.4.479
A Counter Example to Cercignani???s Conjecture for the d Dimensional Kac Model, Journal of Statistical Physics, vol.234, issue.2, pp.1076-1103, 2012. ,
DOI : 10.1007/s10955-012-0565-z
An introduction to Probability Theory and applications, vol. I-II, 1966. ,
Measurability of optimal transportation and convergence rate for Landau type interacting particle systems, Probability Theory and Related Fields, vol.8, issue.2, pp.3-4, 2009. ,
DOI : 10.1007/s00440-007-0128-4
URL : https://hal.archives-ouvertes.fr/hal-00139882
Particle approximation of some Landau equations, Kinetic and Related Models, vol.2, issue.3, pp.451-464, 2009. ,
DOI : 10.3934/krm.2009.2.451
URL : https://hal.archives-ouvertes.fr/hal-00693126
From Newton to Boltzmann : the case of short-range potentials ,
URL : https://hal.archives-ouvertes.fr/hal-00719892
Fourier-Based Distances and Berry-Esseen Like Inequalities for Smooth Densities, Monatshefte f??r Mathematik, vol.135, issue.2, pp.115-136, 2002. ,
DOI : 10.1007/s006050200010
On the kinetic theory of rarefied gases, Communications on Pure and Applied Mathematics, vol.11, issue.4, pp.331-407, 1949. ,
DOI : 10.1002/cpa.3160020403
Factorization for non-symmetric operators and exponential H-Theorem ,
URL : https://hal.archives-ouvertes.fr/hal-00495786
The Landau Equation in a Periodic Box, Communications in Mathematical Physics, vol.231, issue.3, pp.391-434, 2002. ,
DOI : 10.1007/s00220-002-0729-9
Particle approximation of Vlasov equations with singular forces: Propagation of chaos, Annales scientifiques de l'??cole normale sup??rieure, vol.48, issue.4 ,
DOI : 10.24033/asens.2261
N-particles Approximation of the Vlasov Equations with Singular Potential, Archive for Rational Mechanics and Analysis, vol.176, issue.3, pp.489-524, 2007. ,
DOI : 10.1007/s00205-006-0021-9
URL : https://hal.archives-ouvertes.fr/hal-00000670
On Kac's chaos and related problems, Journal of Functional Analysis, vol.266, issue.10 ,
DOI : 10.1016/j.jfa.2014.02.030
Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum, Communications In Mathematical Physics, vol.17, issue.2, pp.189-203, 1986. ,
DOI : 10.1007/BF01211098
Spectral gap for Kac's model of Boltzmann equation, The Annals of Probability, vol.29, issue.1, pp.288-304, 2001. ,
DOI : 10.1214/aop/1008956330
Foundations of kinetic theory, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, pp.171-197, 1954. ,
On the Master???Equation Approach to Kinetic Theory: Linear and Nonlinear Fokker???Planck Equations, Transport Theory and Statistical Physics, vol.1, issue.5-7, pp.5-7, 2004. ,
DOI : 10.1080/00411459408203875
Time evolution of large classical systems, Dynamical systems, theory and applications (Recontres, pp.1-111, 1974. ,
DOI : 10.1007/3-540-07171-7_1
Physical kinetics -course of theoretical physics, 1981. ,
Ricci curvature for metric-measure spaces via optimal transport, Annals of Mathematics, vol.169, issue.3, pp.903-991, 2009. ,
DOI : 10.4007/annals.2009.169.903
The eigenvalues of Kac's master equation, Mathematische Zeitschrift, vol.243, issue.2, pp.291-331, 2003. ,
DOI : 10.1007/s00209-002-0466-y
Propagation of Sobolev regularity for a class of random kinetic models on the real line, Nonlinearity, vol.23, issue.9, pp.2081-2100, 2010. ,
DOI : 10.1088/0951-7715/23/9/003
On the Dynamical Theory of Gases, Philosophical Transactions of the Royal Society of London, vol.157, issue.0, pp.49-88, 1866. ,
DOI : 10.1098/rstl.1867.0004
An exponential formula for solving Boltzmann's equation for a Maxwellian gas, Journal of Combinatorial Theory, vol.2, issue.3, pp.358-382, 1967. ,
DOI : 10.1016/S0021-9800(67)80035-8
On the Kac model for the Landau equation, Kinetic and Related Models, vol.4, issue.1, pp.333-344, 2011. ,
DOI : 10.3934/krm.2011.4.333
Introduction aux limites de champ moyen pour des systèmes de particules. Cours en ligne C.E.L ,
Semigroup factorization in Banach spaces and kinetic hypoellipitic equations ,
Kac???s program in kinetic theory, Inventiones mathematicae, vol.47, issue.3, pp.1-147, 2013. ,
DOI : 10.1007/s00222-012-0422-3
A new approach to quantitative propagation of chaos for drift, diffusion and jump processes, Probability Theory and Related Fields, vol.94, issue.3???4 ,
DOI : 10.1007/s00440-013-0542-8
URL : https://hal.archives-ouvertes.fr/hal-00559132
Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators, Communications in Partial Differential Equations, vol.31, issue.9, pp.1321-1348, 2006. ,
DOI : 10.1080/03605300600635004
URL : https://hal.archives-ouvertes.fr/hal-00087242
Rate of Convergence to Equilibrium for the Spatially Homogeneous Boltzmann Equation with Hard Potentials, Communications in Mathematical Physics, vol.261, issue.3, pp.629-672, 2006. ,
DOI : 10.1007/s00220-005-1455-x
URL : https://hal.archives-ouvertes.fr/hal-00076709
Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff, Journal de Math??matiques Pures et Appliqu??es, vol.87, issue.5, pp.515-535, 2007. ,
DOI : 10.1016/j.matpur.2007.03.003
URL : https://hal.archives-ouvertes.fr/hal-00086958
Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality, Journal of Functional Analysis, vol.173, issue.2, pp.361-400, 2000. ,
DOI : 10.1006/jfan.1999.3557
Information and information stability of random variables and processes. Translated and edited by Amiel Feinstein, 1964. ,
Topics in propagation of chaos, École d'Été de Probabilités de Saint-Flour XIX?1989, pp.165-251, 1991. ,
DOI : 10.1070/SM1974v022n01ABEH001689
Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Z. Wahrsch. Verw. Gebiete, vol.4679, issue.1, pp.67-105, 1978. ,
Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas, J. Statist. Phys, vol.94, pp.3-4, 1999. ,
On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations, Archive for Rational Mechanics and Analysis, vol.187, issue.Ser.2, pp.273-307, 1998. ,
DOI : 10.1007/s002050050106
ON THE SPATIALLY HOMOGENEOUS LANDAU EQUATION FOR MAXWELLIAN MOLECULES, Mathematical Models and Methods in Applied Sciences, vol.08, issue.06, pp.957-983, 1998. ,
DOI : 10.1142/S0218202598000433
DECREASE OF THE FISHER INFORMATION FOR SOLUTIONS OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION WITH MAXWELLIAN MOLECULES, Mathematical Models and Methods in Applied Sciences, vol.10, issue.02, pp.153-161, 2000. ,
DOI : 10.1142/S0218202500000100
A Review of Mathematical Topics in Collisional Kinetic Theory, Handbook of mathematical fluid dynamics, pp.71-305, 2002. ,
DOI : 10.1016/S1874-5792(02)80004-0
Cercignani's Conjecture is Sometimes True and Always Almost True, Communications in Mathematical Physics, vol.234, issue.3, pp.45-490, 2003. ,
DOI : 10.1007/s00220-002-0777-1
Optimal transport, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 2009. ,
DOI : 10.1007/978-3-540-71050-9
URL : https://hal.archives-ouvertes.fr/hal-00974787