2008/09/28 by √Ålvaro Corral, Alvaro Corral · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2009/01/p01022
Submitted to J. Stat. Mech. for the proceedings of UPON 2008 (Lyon), topic: crackling noise
arxiv created 2008/09/28 · openalex publication_date 2009/01/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior as regards the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is obeyed, signaling the existence for those systems of self-similarity in time size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not obey a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double-power-law waiting-time densities. This is somewhat reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.