English

Dynamical Models for Random Simplicial Complexes

Probability 2022-03-22 v3 Combinatorics

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 scale-free nature of Complex Quantum Network Manifolds in dimensions d>2d > 2, and special types of Network Geometry with Flavour models studied in the physics literature by Bianconi, Rahmede [Sci.Rep.  5, 13979 (2015) and Phys.Rev.E  93, 032315 (2016)\mathit{Sci. Rep.} \; \mathbf{5},\text{ 13979 (2015) and }\mathit{Phys. Rev. E} \; \mathbf{93},\text{ 032315 (2016)}].

Keywords

Cite

@article{arxiv.1910.12715,
  title  = {Dynamical Models for Random Simplicial Complexes},
  author = {Nikolaos Fountoulakis and Tejas Iyer and Cécile Mailler and Henning Sulzbach},
  journal= {arXiv preprint arXiv:1910.12715},
  year   = {2022}
}

Comments

53 pages (main body 45 pages), 4 figures. Accepted version, to appear in Annals of Applied Probability

R2 v1 2026-06-23T11:57:14.435Z