Dynamical models for random simplicial complexes

Nikolaos Fountoulakis, Tejas Iyer, Cecile Mailler, Henning Sulzbach

Research output: Contribution to journalArticlepeer-review

Abstract

We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula generalises results for a number of existing models, including random Apollonian networks and the weighted random recursive tree. It also confirms results on the scale-free nature of complex quantum network manifolds in dimensions d>2, and special types of network geometry with Flavour models studied in the physics literature by Bianconi and Rahmede [Sci. Rep. 5 (2015) 13979 and Phys. Rev. E 93 (2016) 032315].
Original languageEnglish
Pages (from-to)2860-2913
Number of pages54
JournalAnnals of Applied Probability
Volume32
Issue number4
Early online date17 Aug 2022
DOIs
Publication statusPublished - 31 Aug 2022

Keywords

  • Complex networks
  • Pólya urns
  • measure valued Pólya processes
  • preferential attachment
  • random recursive trees
  • random simplicial complexes
  • scale-free

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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