Infinite-dimensional diffusions and depletion interaction for a model of colloids

TL;DR

This paper develops a mathematical model for colloids using infinite-dimensional diffusions, revealing how depletion interactions emerge and analyzing their statistical properties and implications for packing and percolation.

Contribution

It introduces a novel infinite-dimensional diffusion framework for the Asakura--Oosawa colloid model, including solutions to SDEs with collision local times and analysis of resulting Gibbs measures.

Findings

Revealed attractive depletion interactions between large colloids.

Connected depletion interactions to percolation and optimal packing.

Constructed solutions to complex stochastic differential equations with collision local times.

Abstract

We consider infinite-dimensional random diffusion dynamics for the Asakura--Oosawa model of interacting hard spheres of two different sizes. We construct a solution to the corresponding SDE with collision local times, analyse its reversible measures, and observe the emergence of an attractive short-range depletion interaction between the large spheres. We study the Gibbs measures associated to this new interaction, exploring connections to percolation and optimal packing.