Polynomial growth in age-dependent branching processes with diverging reproductive number
Alexei Vazquez
Abstract
We study the spreading dynamics on graphs with a power law degree distribution pk ~ k-gamma with 2<gamma<3, as an example of a branching process with diverging reproductive number. We provide evidence that the divergence of the second moment of the degree distribution carries as a consequence a qualitative change in the growth pattern, deviating from the standard exponential growth. First, the population growth is extensive, meaning that the average number of vertices reached by the spreading process becomes of the order of the graph size in a time scale that vanishes in the large graph size limit. Second, the temporal evolution is governed by a polynomial growth, with a degree determined by the characteristic distance between vertices in the graph. These results open a path to further investigation on the dynamics on networks.
Create a lesson
Related papers
Cell-type-specific modularity in E/I networks shapes dynamical regimes and computational capabilities
Emmanouil Giannakakis, Victor Buendía, Oleg Vinogradov et al.
Finite-width shift of the edge of chaos in deep neural networks
Arn Caesar
Neural Networks with Exciton-Polariton Waveguides
Huawen Xu, Ruiqi Bao, Lingyu Tian et al.
Optical Ceiling on Polaron Mobility in Disordered Molecular Semiconductors: Lessons from Eumelanin
Alvan Hunt
Glauber dynamics of the Sherrington--Kirkpatrick spin-glass model: a dynamical cavity method
Grzegorz Szamel
Generative diffusion in long-range correlated landscapes: Speciation cascade and the foam structure of the score
Jerome Garnier-Brun, Giulio Biroli, Marc Mézard et al.