Corrected mean-field model for random sequential adsorption on random geometric graphs

TL;DR

This paper introduces a corrected mean-field model for analyzing the random sequential adsorption of spheres in Euclidean space, using clustered random graphs to better understand spatial correlations and acceptance fractions.

Contribution

The paper proposes a novel approach that compares Euclidean space adsorption to nearest-neighbor blocking on clustered random graphs, providing a more accurate model.

Findings

Characterizes the fraction of accepted spheres using functional limit theorems.

Provides insights into fluctuations of the acceptance fraction.

Introduces a corrected mean-field model for spatial interactions.

Abstract

A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the $d$-dimensional Euclidean space with $d\geq 2$. Spheres arrive sequentially at uniformly chosen locations in space and are accepted only when there is no overlap with previously deposited spheres. Due to spatial correlations, characterizing the fraction of accepted spheres remains largely intractable. We study this fraction by taking a novel approach that compares random sequential adsorption in Euclidean space to the nearest-neighbor blocking on a sequence of clustered random graphs. This random network model can be thought of as a corrected mean-field model for the interaction graph between the attempted spheres. Using functional limit theorems, we characterize the fraction of accepted spheres and its fluctuations.