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 , 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].
Funding Statement
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.
Acknowledgments
This work is part of the Ph.D. thesis of Tejas Iyer and was completed at the University of Birmingham.
Citation
Nikolaos Fountoulakis. Tejas Iyer. Cécile Mailler. Henning Sulzbach. "Dynamical models for random simplicial complexes." Ann. Appl. Probab. 32 (4) 2860 - 2913, August 2022. https://doi.org/10.1214/21-AAP1752
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