Derivation of an Ornstein–Uhlenbeck Process for a Massive Particle in a Rarified Gas of Particles

Alexander, R.: The Infinite Hard Sphere System. Ph.D. dissertation, Dept. Mathematics, Univ. California, Berkeley (1975)

Billingsley, P.: Convergence of Probability Measures. Wiley Series in Probability and Statistics: Probability and Statistics, 2nd edn. Wiley, New York (1999)

Bodineau, T., Gallagher, I., Saint-Raymond, L.: The Brownian motion as the limit of a deterministic system of hard-spheres. Invent Math. 203(2), 493–553 (2016)

Bodineau, T., Gallagher, I., Saint-Raymond, L.: From hard sphere dynamics to the Stokes–Fourier equations: an $$L^2$$ L 2 analysis of the Boltzmann-Grad limit. Ann. PDE 3, 2 (2017)

Caprino, S., Marchioro, C., Pulvirenti, M.: Approach to equilibrium in a microscopic model of friction. Commun. Math. Phys. 264(1), 167–189 (2006)

Cavallaro, G., Marchioro, C.: On the motion of an elastic body in a free gas. Rep. Math. Phys. 69(2), 251–264 (2012)

Cercignani, C., Illner, R., Pulvirenti, M.: The Mathematical Theory of Dilute Gases. Springer, New York (1994)

Dobson, M., Legoll, F., Lelièvre, T., Stoltz, G.: Derivation of Langevin dynamics in a nonzero background flow field. ESAIM: M2AN 47(6), 1583–1626 (2013)

Duplantier, B.: Brownian Motion, Diverse and Undulating. Birkhäuser, Basel (2005)

Dürr, D., Goldstein, S., Lebowitz, J.L.: A mechanical model of Brownian motion. Commun. Math. Phys. 78(4), 507–530 (1981)

Dürr, D., Goldstein, S., Lebowitz, J.L.: A mechanical model for the Brownian motion of a convex body. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 62(4), 427–448 (1983)

Durrett, R.: Stochastic Calculus. A Practical Introduction. Probability and Stochastics Series. CRC Press, Boca Raton (1996)

Gallagher, I., Saint-Raymond, L., Texier, B.: From Newton to Boltzmann: hard spheres and short-range potentials. Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich (2013)

Holley, R.: The motion of a heavy particle in an infinite one dimensional gas of hard spheres. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 17, 181–219 (1971)

Kusuoka, S., Liang, S.: A classical mechanical model of Brownian motion with plural particles. Rev. Math. Phys. 22, 733–838 (2010)

Lanford, O.E.: Time evolution of large classical systems. In: Moser, J. (ed.) Lecture Notes in Physics, vol. 38, pp. 1–111. Springer, New York (1975)

Szász, D., Tóth, B.: Towards a unified dynamical theory of the Brownian particle in an ideal gas. Commun. Math. Phys. 111(1), 41–62 (1987)