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

S. Dhara, J.S.H. van Leeuwaarden, D. Mukherjee

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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≥ 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.

Original languageEnglish
Pages (from-to)872-894
Number of pages23
JournalJournal of Statistical Physics
Volume173
Issue number3-4
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

  • Functional limit theorems
  • Jamming fraction
  • Mean-field analysis
  • Random geometric graph
  • Random sequential adsorption

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