R. Adami, C. Bardos, F. Golse, and A. , Teta: Towards a rigorous derivation of the cubic NLSE in dimension one, Asymptot. Anal, vol.40, issue.2, pp.93-108, 2004.

R. Adami, F. Golse, and A. , Rigorous Derivation of the Cubic NLS in Dimension One, Journal of Statistical Physics, vol.127, issue.6, pp.1193-1220, 2007.
DOI : 10.1007/s10955-006-9271-z

L. V. Ahlfors, Complex analysis. An introduction to the theory of analytic functions of one complex variable, Third edition. International Series in Pure and Applied Mathematics, 1978.

C. Bardos, I. Catto, N. Mauser, and S. Trabelsi, Setting and Analysis of the Multi-configuration Time-dependent Hartree???Fock Equations, Archive for Rational Mechanics and Analysis, vol.37, issue.8, pp.273-330, 2010.
DOI : 10.1007/s00205-010-0308-8

URL : https://hal.archives-ouvertes.fr/hal-00370704

C. Bardos, B. Ducomet, F. Golse, A. Gottlieb, and N. , Mauser: The TDHF approximation for Hamiltonians with m-particle interaction potentials, Commun . Math. Sci, pp.1-9, 2007.

C. Bardos, L. Erdös, F. Golse, N. Mauser, and H. Yau, Derivation of the Schr??dinger???Poisson equation from the quantum -body problem, Comptes Rendus Mathematique, vol.334, issue.6, pp.515-520, 2002.
DOI : 10.1016/S1631-073X(02)02253-7

C. Bardos, F. Golse, and N. Mauser, Weak coupling limit of the N particles Schrödinger equation, Methods Appl. Anal, vol.7, issue.2, pp.275-293, 2000.

C. Bardos, F. Golse, A. Gottlieb, and N. Mauser, Mean field dynamics of fermions and??the??time-dependent??Hartree???Fock equation, Journal de Math??matiques Pures et Appliqu??es, vol.82, issue.6, pp.665-683, 2003.
DOI : 10.1016/S0021-7824(03)00023-0

C. Bardos, F. Golse, A. Gottlieb, and N. , Accuracy of the Time-Dependent Hartree???Fock Approximation for Uncorrelated Initial States, Journal of Statistical Physics, vol.115, issue.3/4, pp.1037-1055, 2004.
DOI : 10.1023/B:JOSS.0000022381.86923.0a

URL : https://hal.archives-ouvertes.fr/hal-00021079

C. Bardos, F. Golse, A. Gottlieb, N. Minneapolis, and . Mn, Mauser: On the derivation of nonlinear Schrödinger and Vlasov equations, in " Dispersive transport equations and multiscale models Mauser: One particle equations for many particle quantum systems: the MCTHDF method, Math. Appl. Quart. Appl. Math, vol.136, issue.1, pp.1-23, 2000.

J. Basdevant and J. Dalibard, Quantum Mechanics, 2005.

J. Batt, N-particle approximation to the nonlinear Vlasov???Poisson system, Nonlinear Analysis: Theory, Methods & Applications, vol.47, issue.3, pp.1445-1456, 2000.
DOI : 10.1016/S0362-546X(01)00280-2

P. Billingsley, Convergence of Probability Measures, 1999.
DOI : 10.1002/9780470316962

F. Bouchut, F. Golse, and C. Pallard, Classical Solutions and the Glassey-Strauss Theorem for the 3D Vlasov-Maxwell System, Archive for Rational Mechanics and Analysis, vol.170, issue.1, pp.1-15, 2003.
DOI : 10.1007/s00205-003-0265-6

F. Bouchut, F. Golse, and C. , Pallard: Nonresonant smoothing for coupled wave + transport equations; applications to the Vlasov-Maxwell system, Rev. Mat. Iberoamericana, vol.20, pp.865-892, 2004.

F. Bouchut, F. Golse, and M. Pulvirenti, Kinetic Equations and Asymptotic Theory, L. Desvillettes et B. Perthame eds, Series in Applied Mathematics , 4. Gauthier-Villars, Editions Scientifiques et Médicales Elsevier, 2000.

A. Bove, G. Daprato, and G. Fano, An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction, Communications in Mathematical Physics, vol.6, issue.3, pp.183-191, 1974.
DOI : 10.1007/BF01646344

A. Bove, G. Daprato, and G. Fano, On the Hartree-Fock time-dependent problem, Communications in Mathematical Physics, vol.78, issue.1, pp.25-33, 1976.
DOI : 10.1007/BF01608633

W. Braun and K. , Hepp: The Vlasov Dynamics and Its Fluctuations in the 1/N Limit of Interacting Classical Particles, Commun. Math. Phys, pp.56-101, 1977.

L. Breiman, Probability, 1968.
DOI : 10.1137/1.9781611971286

H. Brezis, Analyse fonctionnelle. Théorie et applications, 1987.

E. Caglioti, P. Lions, C. Marchioro, and M. , A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, Communications in Mathematical Physics, vol.187, issue.3, pp.501-525, 1992.
DOI : 10.1007/BF02099262

E. Cancès and C. , ON THE TIME-DEPENDENT HARTREE???FOCK EQUATIONS COUPLED WITH A CLASSICAL NUCLEAR DYNAMICS, Mathematical Models and Methods in Applied Sciences, vol.09, issue.07, pp.963-990, 1999.
DOI : 10.1142/S0218202599000440

C. Cercignani, On the Boltzmann equation for rigid spheres, Transport Theory Statist, Phys, vol.2, issue.3, pp.211-225, 1972.

C. Cercignani, R. Illner, and M. Pulvirenti, The mathematical theory of dilute gases, Applied Mathematical Sciences, vol.106, 1994.
DOI : 10.1007/978-1-4419-8524-8

J. M. Chadam and R. T. Glassey, Global existence of solutions to the Cauchy problem for time???dependent Hartree equations, Journal of Mathematical Physics, vol.16, issue.5, pp.1122-1130, 1975.
DOI : 10.1063/1.522642

G. Cottet and P. , On particle-in-cell methods for the Vlasov-Poisson equations, Transport Theory and Statistical Physics, vol.29, issue.1-2, pp.1-31, 1986.
DOI : 10.1137/0721003

R. Dobrushin, Vlasov equations, Functional Analysis and Its Applications, vol.5, issue.3, pp.115-123, 1979.
DOI : 10.1007/BF01077243

A. Elgart, L. Erdös, B. Schlein, and H. Yau, Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons, Archive for Rational Mechanics and Analysis, vol.179, issue.2, pp.265-283, 2006.
DOI : 10.1007/s00205-005-0388-z

Y. Elskens, M. K. Kießling, and V. Ricci, The Vlasov Limit for a System of Particles which Interact with a Wave Field, Communications in Mathematical Physics, vol.30, issue.2, pp.673-712, 2009.
DOI : 10.1007/s00220-008-0591-5

L. Erdös and H. Yau, Derivation of the nonlinear Schr??dinger equation from a many-body Coulomb system, Advances in Theoretical and Mathematical Physics, vol.5, issue.6, pp.1169-1205, 2001.
DOI : 10.4310/ATMP.2001.v5.n6.a6

L. Erdös, B. Schlein, and H. Yau, Derivation of the cubic non-linear Schr??dinger equation from quantum dynamics of many-body systems, Inventiones mathematicae, vol.116, issue.4, pp.515-614, 2007.
DOI : 10.1007/s00222-006-0022-1

L. Erdös, B. Schlein, and H. Yau, Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate, Annals of Mathematics, vol.172, issue.1, pp.172-291, 2010.
DOI : 10.4007/annals.2010.172.291

J. Fröhlich, A. Knowles, and S. Schwarz, On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction, Communications in Mathematical Physics, vol.56, issue.17, pp.1023-1059, 2009.
DOI : 10.1007/s00220-009-0754-z

J. Fröhlich and A. Knowles, A Microscopic Derivation of the Time-Dependent Hartree-Fock Equation with Coulomb Two-Body Interaction, Journal of Statistical Physics, vol.56, issue.4, pp.23-50, 2011.
DOI : 10.1007/s10955-011-0311-y

I. Gallagher, L. Saint-raymond, and B. , Texier: From Newton to Boltzmann: the case of hard sphere potentials, preprint arXiv, pp.1208-5753

P. Gérard, Equations de champ moyen pour la dynamique quantique d'un grand nombre de particules (d'après Bardos, Exp. no. 930, pp.147-164, 2003.

]. J. Ginibre and G. Velo, On a class of non linear Schr???dinger equations with non local interaction, Mathematische Zeitschrift, vol.16, issue.2, pp.109-145, 1980.
DOI : 10.1007/BF01214768

J. Ginibre and G. , The classical field limit of scattering theory for non-relativistic many-boson systems. I, Communications In Mathematical Physics, vol.14, issue.1, pp.37-76, 1979.
DOI : 10.1007/BF01197745

R. T. Glassey, The Cauchy problem in kinetic theory, Society for Industrial and Applied Mathematics (SIAM), 1996.
DOI : 10.1137/1.9781611971477

F. Golse, The Mean-Field Limit for the Dynamics of Large Particle Systems, Journées Equations aux Dérivées Partielles, 2003.

F. Golse, The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics, Communications in Mathematical Physics, vol.8, issue.3, pp.310-789, 2012.
DOI : 10.1007/s00220-011-1377-8

URL : https://hal.archives-ouvertes.fr/hal-00545569

F. Golse, C. Mouhot, and V. Ricci, Empirical measures and mean field hierarchies

J. Goodman, T. Hou, and J. , Convergence of the point vortex method for the 2-D euler equations, Communications on Pure and Applied Mathematics, vol.25, issue.3, pp.415-430, 1990.
DOI : 10.1002/cpa.3160430305

J. Goodman and T. , New stability estimates for the 2-D vortex method, Communications on Pure and Applied Mathematics, vol.24, issue.8-9, pp.1015-1031, 1991.
DOI : 10.1002/cpa.3160440813

F. A. Grünbaum, Propagation of chaos for the Boltzmann equation, Archive for Rat, Mech. Anal, vol.42, pp.323-345, 1971.

M. Hauray, WASSERSTEIN DISTANCES FOR VORTICES APPROXIMATION OF EULER-TYPE EQUATIONS, Mathematical Models and Methods in Applied Sciences, vol.19, issue.08, pp.1357-1384, 2009.
DOI : 10.1142/S0218202509003814

M. Hauray and P. , 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

M. Hauray and P. , Jabin: Propagation of chaos for particles approximations of Vlasov equations with singular forces

K. Hepp, The classical limit for quantum mechanical correlation functions, Communications in Mathematical Physics, vol.67, issue.4, pp.265-277, 1974.
DOI : 10.1007/BF01646348

E. Hewitt and L. J. Savage, Symmetric measures on Cartesian products, Transactions of the American Mathematical Society, vol.80, issue.2, pp.470-501, 1955.
DOI : 10.1090/S0002-9947-1955-0076206-8

L. Hörmander, The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis, Classics in Mathematics, 2003.

L. Hörmander, The analysis of linear partial differential operators. III. Pseudo-differential operators, Classics in Mathematics, 2007.

L. Hörmander, The analysis of linear partial differential operators. IV. Fourier integral operators, Classics in Mathematics, 2009.

L. Hörmander, Lectures on nonlinear hyperbolic differential equations, Mathmatiques & Applications, vol.26, 1997.

J. Horowitz and R. Karandikar, Mean rates of convergence of empirical measures in the Wasserstein metric, Journal of Computational and Applied Mathematics, vol.55, issue.3, pp.261-273, 1994.
DOI : 10.1016/0377-0427(94)90033-7

M. Kac, Foundations of kinetic theory, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, pp.171-197, 1954.

T. Kato, Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc, vol.70, pp.195-211, 1951.

T. Kato, Perturbation theory for linear operators, Classics in Mathematics, 1995.

M. K. and -. Kießling, Statistical mechanics of classical particles with logarithmic interactions, Communications on Pure and Applied Mathematics, vol.6, issue.1, pp.27-56, 1993.
DOI : 10.1002/cpa.3160460103

S. Klainerman and M. , On the Uniqueness of Solutions to the Gross-Pitaevskii Hierarchy, Communications in Mathematical Physics, vol.120, issue.5, pp.169-185, 2008.
DOI : 10.1007/s00220-008-0426-4

A. Knowles and P. , Mean-Field Dynamics: Singular Potentials and Rate of Convergence, Communications in Mathematical Physics, vol.53, issue.3, pp.101-138, 2010.
DOI : 10.1007/s00220-010-1010-2

L. Landau and E. Lifshitz, Quantum mechanics: non-relativistic theory Translated from the Russian by, Course of Theoretical Physics, 1958.

O. Lanford, Time evolution of large classical systems, Battelle Res. Inst. Lecture Notes in Phys, vol.38, pp.1-111, 1974.
DOI : 10.1007/3-540-07171-7_1

E. H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems, Communications in Mathematical Physics, vol.22, issue.3, pp.185-194, 1977.
DOI : 10.1007/BF01609845

P. Lions and B. , Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Inventiones Mathematicae, vol.33, issue.no 1, pp.415-430, 1991.
DOI : 10.1007/BF01232273

P. Malliavin, H. Airault, L. Kay, and G. Letac, Integration and Probability, Graduate Texts in Math, vol.157, 1995.
DOI : 10.1007/978-1-4612-4202-4

C. Marchioro and M. Pulvirenti, Mathematical Theory of Incompressible Nonviscous Fluids, 1994.
DOI : 10.1007/978-1-4612-4284-0

S. Mischler and C. Mouhot, Kacs program in kinetic theory, Invent. Math., published online, pp.10-1007

S. Mischler, C. Mouhot, and B. , Wennberg: A new approach to quantitative propagation of chaos for drift, diffusion and jump processes, preprint arXiv 1101, p.4727

H. Narnhoffer and G. Sewell, Vlasov hydrodynamics of a quantum mechanical model, Communications in Mathematical Physics, vol.71, issue.1, pp.9-24, 1981.
DOI : 10.1007/BF01208282

H. Neunzert and J. Wick, Die Approximation der L??sung von Integro-Differentialgleichungen durch endliche Punktmengen, Lecture Notes in Math, vol.395, pp.275-290, 1974.
DOI : 10.1007/BFb0060678

L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, Journal of Differential Geometry, vol.6, issue.4, pp.561-576, 1972.
DOI : 10.4310/jdg/1214430643

T. Nishida, A note on a theorem of Nirenberg, Journal of Differential Geometry, vol.12, issue.4, pp.629-633, 1977.
DOI : 10.4310/jdg/1214434231

L. V. Ovcyannikov, A nonlinear Cauchy problem in a scale of Banach spaces. (Russian) Dokl. Akad, Nauk SSSR, vol.200, pp.789-792, 1971.

K. Pfaffelmoser, Global classical soutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eq, pp.95-281, 1992.

S. Rachev and L. Rüschendorf, Mass transportation problems. Vol. I. Theory, Probability and its Applications, 1998.

G. Rein, Global Weak Solutions to the Relativistic Vlasov-Maxwell System Revisited, Communications in Mathematical Sciences, vol.2, issue.2, pp.145-158, 2004.
DOI : 10.4310/CMS.2004.v2.n2.a1

G. Rein, Collisionless kinetic equations from astrophysicsthe Vlasov- Poisson system, Handbook of differential equations: evolutionary equations, Handb. Differ. Equ, vol.III, pp.383-476, 2007.

I. Rodnianski and B. , Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics, Communications in Mathematical Physics, vol.52, issue.3, pp.31-61, 2009.
DOI : 10.1007/s00220-009-0867-4

S. Schochet, The point-vortex method for periodic weak solutions of the 2-D Euler equations, Communications on Pure and Applied Mathematics, vol.49, issue.9, pp.911-965, 1996.
DOI : 10.1002/(SICI)1097-0312(199609)49:9<911::AID-CPA2>3.0.CO;2-A

J. Shatah and M. Struwe, Geometric wave equations, Courant Lecture Notes in Mathematics, vol.2, 1998.
DOI : 10.1090/cln/002

H. Spohn, Kinetic equations from hamiltonian dynamics, Rev. Mod. Phys, vol.52, issue.3, pp.600-640, 1980.
DOI : 10.1103/revmodphys.52.569

H. Spohn, On the Vlasov hierarchy, Mathematical Methods in the Applied Sciences, vol.56, issue.1, p.445455, 1981.
DOI : 10.1002/mma.1670030131

H. Spohn, Large scale dynamics of interacting particles
DOI : 10.1007/978-3-642-84371-6

A. Sznitman, Topics in propagation of chaos, Ecole d'´ eté de Probabilités de Saint-Flour XIX?1989, Lecture Notes in Math, pp.165-251, 1464.

S. Ukai, The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem, Japan Journal of Industrial and Applied Mathematics, vol.12, issue.2, pp.383-392, 2001.
DOI : 10.1007/BF03168581

S. Ukai and T. , Okabe: On classical solutions in the large in time of two dimensional Vlasov's equation, Osaka J. Math, vol.15, pp.245-261, 1978.

C. Villani, Topics in Optimal Transportation, American Math. Soc. Providence RI, vol.58, 2003.
DOI : 10.1090/gsm/058

C. Villani, Optimal Transport: Old and New, 2009.
DOI : 10.1007/978-3-540-71050-9

S. Wollman, On the Approximation of the Vlasov--Poisson System by Particle Methods, SIAM Journal on Numerical Analysis, vol.37, issue.4, pp.1369-1398, 2000.
DOI : 10.1137/S0036142999298528