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

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 $d\ge 2$. 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.

23 pages, 5 figures; This version contains major updates in the exposition of the paper

References in corpus (9)

• Random graphs with clustering
• Random graphs containing arbitrary distributions of subgraphs
• Epidemic spreading on complex networks with community structures
• Martingale proofs of many-server heavy-traffic limits for Markovian queues
• Gaussian limits for random measures in geometric probability
• Clustering implies geometry in networks
• Power-law relations in random networks with communities
• Moderate deviations for some point measures in geometric probability
• Generalized random sequential adsorption on Erdős-Rényi random graphs

Cited by in corpus (1)

• Modeling Rydberg Gases using Random Sequential Adsorption on Random Graphs