Return distributions in dog-flea model revisited

Burhan Bakar and Ugur Tirnakli

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 17, 3382-3386

Abstract: A recent study of coherent noise model for the system size independent case provides an exact relation between the exponent τ of avalanche size distribution and the q value of the appropriate q-Gaussian that fits the return distribution of the model. This relation is applied to Ehrenfest’s historical dog-flea model by treating the fluctuations around the thermal equilibrium as avalanches. We provide a clear numerical evidence that the relation between the exponent τ of fluctuation length distribution and the q value of the appropriate q-Gaussian obeys this exact relation when the system size is large enough. This allows us to determine the value of the q-parameter a priori from one of the well known exponents of such dynamical systems. Furthermore, it is shown that the return distribution in dog-flea model gradually approaches q-Gaussian as the system size increases and this tendency can be analyzed by a well defined analytical expression.

Keywords: Fluctuation phenomena; Time series analysis; Self-organized criticality (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:17:p:3382-3386

DOI: 10.1016/j.physa.2010.04.037

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