Dynamical models for random simplicial complexes

Dynamical models for random simplicial complexes

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 re...

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Veröffentlicht in:The Annals of applied probability 2022-08, Vol.32 (4), p.2860
Hauptverfasser: Fountoulakis, Nikolaos, Iyer, Tejas, Mailler, Cécile, Sulzbach, Henning
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic methods
Asymptotic properties
Dynamic models
Dynamical systems
Flavors
Mathematical models
Random variables
Random walk theory
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Beschreibung
Zusammenfassung: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].
ISSN:1050-5164
2168-8737
DOI:10.1214/21-AAP1752