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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 11: Networks - From Topology to Dynamics I (joint SOE/DY/BP)

SOE 11.1: Talk

Wednesday, March 18, 2020, 17:30–17:45, GÖR 226

Scaling and Fluctuation Scaling in Systems and Networks of Constant Size — •Cornelia Metzig¹ and Caroline Colijn² — ¹Queen Mary University of London, UK — ²Simon Fraser University, Burnaby, Canada

We propose a preferential-attachment-type model for a system of constant size which applies to urn/ball systems and to networks. It generates a power law for the size (or degree) distribution with exponential cutoff depending on parameters. This distribution can be explained by maximization of the Gibbs-Shannon entropy for one iteration of the stochastic process. We use as constraint the information on the growth of individual urns. Alternatively it is possible to calculate the exact probabilities. Another distribution that often occurs together with power laws, a `tent-shaped' growth rate distribution, comes out naturally from this model. We confirm our theoretical results with numerical simulations and by another method using recursively calculated exact probabilities.