Dynamical Models for Random Simplicial Complexes

TL;DR

This paper introduces a comprehensive model for random dynamical simplicial complexes, deriving an asymptotic degree distribution that unifies various existing models and confirms scale-free properties in higher-dimensional quantum network structures.

Contribution

It provides a general formula for the asymptotic degree distribution of random simplicial complexes, encompassing multiple models and confirming scale-free behavior in complex quantum network manifolds.

Findings

Derived a unifying asymptotic degree distribution formula

Confirmed scale-free nature of high-dimensional quantum network models

Included models like random Apollonian networks and weighted recursive trees

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