Analysis of return distributions in the coherent noise model

TL;DR

This paper investigates the return distributions in the coherent noise model, revealing they follow q-Gaussian forms and establishing a relation between avalanche size exponents and q-values, supported by numerical evidence.

Contribution

It introduces an exact relation between avalanche size exponent and q-Gaussian parameter, linking statistical mechanics with the model's avalanche behavior.

Findings

Return distributions are q-Gaussians in the size-independent case.

The relation q=(tau+2)/tau connects avalanche exponent and distribution shape.

Numerical results support the analytical relation and size effect analysis.

Abstract

The return distributions of the coherent noise model are studied for the system size independent case. It is shown that, in this case, these distributions are in the shape of q-Gaussians, which are the standard distributions obtained in nonextensive statistical mechanics. Moreover, an exact relation connecting the exponent $\tau$ of avalanche size distribution and the q value of appropriate q-Gaussian has been obtained as q=(tau+2)/tau. Making use of this relation one can easily determine the q parameter values of the appropriate q-Gaussians a priori from one of the well-known exponents of the system. Since the coherent noise model has the advantage of producing different tau values by varying a model parameter \sigma, clear numerical evidences on the validity of the proposed relation have been achieved for different cases. Finally, the effect of the system size has also been analysed and an analytical expression has been proposed, which is corroborated by the numerical results.