Dynamical models for random simplicial complexes

Nikolaos Fountoulakis, Tejas Iyer, Cecile Mailler, Henning Sulzbach

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We introduce and 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.
Original languageEnglish
Pages (from-to)2860-2913
Number of pages54
JournalAnnals of Applied Probability
Issue number4
Early online date17 Aug 2022
Publication statusPublished - Aug 2022


  • random simplicial complexes
  • preferential attachment
  • complex networks
  • Polya processes
  • measure-valued processes
  • random recursive trees


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