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 encompasses results for a number of existing models, including random Apollonian networks and the weighted random recursive tree. It also confirms results on the scalefree 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, Rahmede [$\mathit{Sci. Rep.} \; \mathbf{5},\text{ 13979 (2015) and }\mathit{Phys. Rev. E} \; \mathbf{93},\text{ 032315 (2016)}$].
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.12715
 Bibcode:
 2019arXiv191012715F
 Keywords:

 Mathematics  Probability;
 Mathematics  Combinatorics;
 90B15;
 60J20;
 05C80
 EPrint:
 45 pages (main body 37 pages), 4 figures