Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect

Abstract

We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in ${\mathbb{R}}^d$, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is the occurrence of an attractive short-range dynamical interaction -- known in the physics literature as a depletion interaction -- between the large spheres, which is induced by the hidden presence of the small ones. By considering the asymptotic limit for such a system when the density of the particles is high, we also obtain a constructive dynamical approach to the famous discrete geometry problem of maximisation of the contact number of $n$ identical spheres in ${\mathbb{R}}^d$. As support material, we propose numerical simulations in the form of movies.

arXiv commentVersion accepted for publication in Stochastic Processes and their Applications. 27 pages, 6 figures

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Cited by in corpus (1)

• The variational principle for a marked Gibbs point process with infinite-range multibody interactions