R. Alexander, The Infinite Hard Sphere System, 1975.

R. Alexander, Time evolution for infinitely many hard spheres, Communications in Mathematical Physics, vol.29, issue.3, p.217232, 1976.
DOI : 10.1007/BF01608728

C. Bardos, Probì emes aux limites pour les quations aux dérivées partielles du premier ordrè a coefficients réels; théorèmes d'approximation; applicationàapplicationà l'´ equation de transport, Ann. Sci. ´ Ecole Norm. Sup, vol.4, pp.3-185, 1970.

C. Bardos, F. Golse, and C. D. , Levermore: Fluid Dynamic Limits of the Boltzmann Equation I, J. Stat, Phys, pp.63-323, 1991.

C. Bardos, F. Golse, and C. D. , Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation, Communications on Pure and Applied Mathematics, vol.82, issue.162, pp.667-753, 1993.
DOI : 10.1002/cpa.3160460503

C. Bardos, R. Santos, and R. Sentis, Diffusion approximation and computation of the critical size, Transactions of the American Mathematical Society, vol.284, issue.2, pp.617-649, 1984.
DOI : 10.1090/S0002-9947-1984-0743736-0

H. Van-beijeren, O. E. Iii-lanford, J. Lebowitz, and H. Spohn, Equilibrium time correlation functions in the low-density limit, Journal of Statistical Physics, vol.54, issue.2, pp.237-257, 1980.
DOI : 10.1007/BF01008050

P. Billingsley, Probability and measure, Probability and Mathematical Statistics, 1995.

C. Boldrighini, L. A. Bunimovich, and Y. Sinai, On the Boltzmann equation for the Lorentz gas, Journal of Statistical Physics, vol.78, issue.3, pp.477-501, 1983.
DOI : 10.1007/BF01008951

L. A. Bunimovich and Y. G. Sinai, Statistical properties of lorentz gas with periodic configuration of scatterers, Communications in Mathematical Physics, vol.1, issue.2, pp.479-497, 1980.
DOI : 10.1007/BF02046760

E. Caglioti and F. Golse, On the Distribution of Free Path Lengths for the Periodic Lorentz Gas III, Communications in Mathematical Physics, vol.236, issue.2, pp.199-221, 2003.
DOI : 10.1007/s00220-003-0825-5
URL : https://hal.archives-ouvertes.fr/hal-00119070

E. Caglioti and F. Golse, On the Boltzmann-Grad Limit for??the??Two Dimensional Periodic Lorentz Gas, Journal of Statistical Physics, vol.1, issue.3, pp.264-317, 2010.
DOI : 10.1007/s10955-010-0046-1
URL : https://hal.archives-ouvertes.fr/hal-00454029

C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases, 1994.
DOI : 10.1007/978-1-4419-8524-8

W. De-roeck and J. Fröhlich, Diffusion of a Massive Quantum Particle Coupled to a Quasi-Free Thermal Medium, Communications in Mathematical Physics, vol.21, issue.1, pp.613-707, 2011.
DOI : 10.1007/s00220-011-1222-0

L. Desvillettes and F. Golse, A remark concerning the Chapman-Enskog asymptotics, in Advances in kinetic theory and computing, Adv. Math. Appl. Sci. NJ, vol.22, pp.191-203, 1994.

L. Desvillettes and M. Pulvirenti, THE LINEAR BOLTZMANN EQUATION FOR LONG-RANGE FORCES: A DERIVATION FROM PARTICLE SYSTEMS, Mathematical Models and Methods in Applied Sciences, vol.09, issue.08, p.11231145, 1999.
DOI : 10.1142/S0218202599000506

L. Desvillettes and V. Ricci, A rigorous derivation of a linear kinetic equation of Fokker-Planck type in the limit of grazing collisions, J. Statist. Phys, vol.104, pp.5-6, 2001.

L. Erd?-os, Lecture notes on quantum Brownian motion, Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School, 2010.

L. Erd?-os, M. Salmhofer, and H. T. Yau, Quantum diffusion of the random Schrodinger evolution in the scaling limit, Acta mathematica, pp.211-278, 2008.

R. Esposito, R. Marra, and H. T. Yau, Navier-Stokes equations for stochastic particle systems on the lattice, Communications in Mathematical Physics, vol.118, issue.2, pp.395-456, 1996.
DOI : 10.1007/BF02517896

I. Gallagher, L. Saint-raymond, and B. Texier, From Newton to Boltzmann : the case of hard-spheres and short-range potentials
DOI : 10.4171/129

G. Gallavotti, Statistical mechanics. A short treatise. Texts and Monographs in Physics, 1999.

F. Golse, On the Periodic Lorentz Gas and the Lorentz Kinetic Equation, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.17, issue.4, pp.735-749, 2008.
DOI : 10.5802/afst.1200
URL : https://hal.archives-ouvertes.fr/hal-00138843

D. Hilbert, Begründung der kinetischen Gastheorie. (German) Math, Ann, vol.72, issue.4, pp.562-577, 1912.

F. King, BBGKY hierarchy for positive potentials, 1975.

T. Komorowski, C. Landim, and S. Olla, Fluctuations in Markov processes. Time symmetry and martingale approximation, Grundlehren der Mathematischen Wissenschaften
URL : https://hal.archives-ouvertes.fr/hal-00722537

O. E. Lanford, Time evolution of large classical systems, Lect. Notes in Physics, vol.38, pp.1-111, 1975.
DOI : 10.1007/3-540-07171-7_1

J. Lebowitz and H. Spohn, Microscopic basis for Fick's law for self-diffusion, Journal of Statistical Physics, vol.78, issue.3, pp.539-556, 1982.
DOI : 10.1007/BF01008323

J. Lebowitz and H. Spohn, Steady state self-diffusion at low density, Journal of Statistical Physics, vol.21, issue.1, pp.39-55, 1982.
DOI : 10.1007/BF01008247

H. Lorentz, Le mouvement desélectronsdesélectrons dans les métaux, Arch. Neerl, vol.10, pp.336-371, 1905.

J. Marklof, KINETIC TRANSPORT IN CRYSTALS, XVIth International Congress on Mathematical Physics, pp.162-179, 2009.
DOI : 10.1142/9789814304634_0009

J. Marklof and A. Strömbergsson, The Boltzmann-Grad limit of the periodic Lorentz gas, Annals of Mathematics, vol.174, issue.1, pp.225-298, 2011.
DOI : 10.4007/annals.2011.174.1.7

J. Marklof and B. Toth, Superdiffusion in the periodic Lorentz gas, arXiv:1403, p.preprint, 2014.

R. Pettersson, On weak and strong convergence to equilibrium for solutions to the linear Boltzmann equation, Journal of Statistical Physics, vol.315, issue.1-2, pp.355-380, 1993.
DOI : 10.1007/BF01048054

S. Olla, S. Varadhan, and H. Yau, Hydrodynamical limit for a Hamiltonian system with weak noise, Communications in Mathematical Physics, vol.129, issue.3, pp.523-560, 1993.
DOI : 10.1007/BF02096727

M. Pulvirenti, C. Saffirio, and S. Simonella, On the validity of the Boltzmann equation for short range potentials, Reviews in Mathematical Physics, vol.26, issue.02, 2014.
DOI : 10.1142/S0129055X14500019

J. Quastel and H. Yau, Lattice Gases, Large Deviations, and the Incompressible Navier-Stokes Equations, The Annals of Mathematics, vol.148, issue.1, pp.51-108, 1998.
DOI : 10.2307/120992

L. Saint-raymond, Hydrodynamic limits of the Boltzmann equation, Lecture Notes in Mathematics, vol.1971, 1971.
DOI : 10.1007/978-3-540-92847-8

S. Simonella, Evolution of Correlation Functions in the Hard Sphere Dynamics, Journal of Statistical Physics, vol.18, issue.2, pp.1191-1221, 2014.
DOI : 10.1007/s10955-013-0905-7

H. Spohn, The Lorentz process converges to a random flight process, Communications in Mathematical Physics, vol.25, issue.3, pp.277-290, 1978.
DOI : 10.1007/BF01612893

H. Spohn, Large scale dynamics of interacting particles, 1991.
DOI : 10.1007/978-3-642-84371-6

D. Szasz and B. Toth, Towards a unified dynamical theory of the Brownian particle in an ideal gas, Communications in Mathematical Physics, vol.104, issue.1, pp.41-62, 1987.
DOI : 10.1007/BF01239014

K. Uchiyama, Derivation of the Boltzmann equation from particle dynamics, Hiroshima Math, J, vol.18, issue.2, pp.245-297, 1988.