Dynamical models for random simplicial complexes

Nikolaos Fountoulakis; Tejas Iyer; Cecile Mailler; Henning Sulzbach

doi:10.1214/21-AAP1752

Dynamical models for random simplicial complexes

Nikolaos Fountoulakis, Tejas Iyer, Cecile Mailler, Henning Sulzbach

Mathematics

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Abstract

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 language	English
Pages (from-to)	2860-2913
Number of pages	54
Journal	Annals of Applied Probability
Volume	32
Issue number	4
Early online date	17 Aug 2022
DOIs	https://doi.org/10.1214/21-AAP1752
Publication status	Published - Aug 2022

Keywords

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

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10.1214/21-AAP1752Licence: None: All rights reserved

FountoulakisN2021Dynamical
This is the authors accepted manuscript (AAM) for an article published in Annals of Applied Probability, 32(4): 2860-2913 (August 2022). DOI: 10.1214/21-AAP1752, published by Institute of Mathematical Statistics https://imstat.org/journals-and-publications/annals-of-applied-probability/.
Accepted author manuscript, 855 KBLicence: None: All rights reserved

Dynamic models of random simplicial complexes
Fountoulakis, N. (Principal Investigator)
Engineering & Physical Science Research Council
3/12/17 → 2/12/20
Project: Research Councils

Cite this

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abstract = "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.",

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N2 - 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.

AB - 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.

KW - random simplicial complexes

KW - preferential attachment

KW - complex networks

KW - Polya processes

KW - measure-valued processes

KW - random recursive trees

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DO - 10.1214/21-AAP1752

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EP - 2913

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 4

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Dynamical models for random simplicial complexes

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Keywords

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Dynamic models of random simplicial complexes

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