IIASA RepositoryExtreme robustness of scaling in sample space reducing processes explains Zipf’s law in diffusion on directed networksB.Corominas-MurtraauthorR.HanelauthorS.ThurnerauthorIt 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.2016ElsevierArticle

For work being deposited by its own author: In self-archiving this collection of files and associated bibliographic metadata, I grant IIASA Repository the right to store them and to make them permanently available publicly for free on-line. I declare that this material is my own intellectual property and I understand that IIASA Repository does not assume any responsibility if there is any breach of copyright in distributing these files or metadata. (All authors are urged to prominently assert their copyright on the title page of their work.)

For work being deposited by someone other than its author: I hereby declare that the collection of files and associated bibliographic metadata that I am archiving at IIASA Repository) is in the public domain. If this is not the case, I accept full responsibility for any breach of copyright that distributing these files or metadata may entail.

Clicking on the deposit button indicates your agreement to these terms.