2016/02/29 by Bernat Corominas-Murtra, Bernat Corominas‐Murtra, Rudolf Hanel +1 · 17 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Diffusion #Exponent #Law #Mathematics #Physics #Power law #Scaling #Statistical physics #Statistics #Stochastic process #Theoretical and Computational Physics #Zipf's law #cond-mat.dis-nn #physics.soc-ph
paper · pdf · doi:10.1088/1367-2630/18/9/093010
published in New Journal of Physics 18(9), 093010 (IOP Publishing) · 11 pages, 5 figures
arxiv created 2016/06/24 · openalex created_date 2016/06/24 · openalex publication_date 2016/09/06 · arxiv updated 2017/10/02 · openalex updated_date 2026/08/06
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such sample space reducing processes offer an alternative new mechanism to understand the emergence of scaling in countless processes. The corresponding power law exponents were shown to be related to noise levels in the process. Here we show that the emergence of scaling is not limited to the simplest SSRPs, but holds for a huge domain of stochastic processes that are characterised by non-uniform prior distributions. We demonstrate mathematically that in the absence of noise the scaling exponents converge to −1 (Zipf's law) for almost all prior distributions. As a consequence it becomes possible to fully understand targeted diffusion on weighted directed networks and its associated scaling laws in node visit distributions. The presence of cycles can be properly interpreted as playing the same role as noise in SSRPs and, accordingly, determine the scaling exponents. The result that Zipf's law emerges as a generic feature of diffusion on networks, regardless of its details, and that the exponent of visiting times is related to the amount of cycles in a network could be relevant for a series of applications in traffic-, transport- and supply chain management.