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

University of Birmingham

Research output: Contribution to journal › Article › peer-review

5 Citations (SciVal)

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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 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 - 31 Aug 2022

Bibliographical note

Funding Information:
Funding. Nikolaos Fountoulakis was supported by the EPSRC, grant EP/P026729/1, and the Alan Turing Institute, grant EP/N510129/1. Cécile Mailler was supported by the EPSRC fellowship EP/R022186/1.

Funding Information:
This work is part of the Ph.D. thesis of Tejas Iyer and was completed at the University of Birmingham. Funding. Nikolaos Fountoulakis was supported by the EPSRC, grant EP/P026729/1, and the Alan Turing Institute, grant EP/N510129/1. Cécile Mailler was supported by the EPSRC fellowship EP/R022186/1.

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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10.1214/21-AAP1752

Random_Dynamical_Simplices (15).PDFAccepted author manuscript, 859 KB

https://arxiv.org/pdf/1910.12715.pdf

Cite this

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title = "Dynamical models for random simplicial complexes",

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].",

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note = "Funding Information: Funding. Nikolaos Fountoulakis was supported by the EPSRC, grant EP/P026729/1, and the Alan Turing Institute, grant EP/N510129/1. C{\'e}cile Mailler was supported by the EPSRC fellowship EP/R022186/1. Funding Information: This work is part of the Ph.D. thesis of Tejas Iyer and was completed at the University of Birmingham. Funding. Nikolaos Fountoulakis was supported by the EPSRC, grant EP/P026729/1, and the Alan Turing Institute, grant EP/N510129/1. C{\'e}cile Mailler was supported by the EPSRC fellowship EP/R022186/1. ",

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AU - Mailler, Cecile

AU - Sulzbach, Henning

N1 - Funding Information: Funding. Nikolaos Fountoulakis was supported by the EPSRC, grant EP/P026729/1, and the Alan Turing Institute, grant EP/N510129/1. Cécile Mailler was supported by the EPSRC fellowship EP/R022186/1. Funding Information: This work is part of the Ph.D. thesis of Tejas Iyer and was completed at the University of Birmingham. Funding. Nikolaos Fountoulakis was supported by the EPSRC, grant EP/P026729/1, and the Alan Turing Institute, grant EP/N510129/1. Cécile Mailler was supported by the EPSRC fellowship EP/R022186/1.

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KW - measure valued Pólya processes

KW - preferential attachment

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KW - scale-free

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Dynamical models for random simplicial complexes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Fellowship - Random trees: analysis and applications

Cite this

Dynamical models for random simplicial complexes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Fellowship - Random trees: analysis and applications

Cite this