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The Brownian motion as the limit of a deterministic system of hard-spheres | | Thierry Bodineau
; Isabelle Gallagher
; Laure Saint-Raymond
; | | Date: |
15 May 2013 | | Abstract: | We provide a rigorous derivation of the brownian motion as the hydrodynamic
limit of systems of hard-spheres as the number of particles $N$ goes to
infinity and their diameter $varepsilon$ simultaneously goes to 0, in the fast
relaxation limit $N varepsilon^{d-1} o infty$ (with a suitable scaling of
the observation time and length). As suggested by Hilbert in his sixth problem,
we use the linear Boltzmann equation as an intermediate level of description
for one tagged particle in a gas close to global equilibrium. Our proof relies
on the fundamental ideas of Lanford. The main novelty here is the detailed
study of the branching process, leading to explicit estimates on pathological
collision trees. | | Source: | arXiv, 1305.3397 | | Services: | Forum | Review | PDF | Favorites | |
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