RT Journal Article
SR 00
ID 10.1088/1367-2630/18/9/093010
A1 Corominas-Murtra, B.
A1 Hanel, R.
A1 Thurner, S.
T1 Extreme robustness of scaling in sample space reducing processes explains Zipf’s law in diffusion on directed networks
JF New Journal of Physics
YR 2016
FD 2016
VO 18
IS 9
SP 093010
K1 network diffusion; path dependence; random walks; sample space reducing processes; scaling laws; Zipfs law
AB 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.
PB Elsevier
SN 1367-2630
LK https://pure.iiasa.ac.at/id/eprint/13885/