Point-occurrence self-similarity in crackling-noise systems and in other complex systems
Corral Cano, Álvaro (Centre de Recerca Matemàtica)
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Publicación: Centre de Recerca Matemàtica 2008
Descripción: 19 p.
Resumen: It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding 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 fulfilled, signaling the existence on 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 fulfill 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 somehow 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.
Derechos: Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús Creative Commons
Lengua: Anglès.
Colección: Prepublicacions del Centre de Recerca Matemàtica
Colección: Prepublicacions del Centre de Recerca Matemàtica ; 834
Documento: article ; submittedVersion

Adreça alternativa: https://hdl.handle.net/2072/15543


19 p, 145.3 KB

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