DYNAMICAL MODELS FOR RANDOM SIMPLICIAL COMPLEXES

• 成果类型: Article
• 署名作者: Fountoulakis, Nikolaos; Iyer, Tejas; Mailler, Cecile; Sulzbach, Henning
• 署名单位: University of Birmingham; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bath
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1752
• 发表日期: 2022
• 页码: 2860-2913
• 关键词: branching-processes; recursive trees; LIMIT-THEOREMS; CONVERGENCE; distances

摘要

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].