再论狗蚤模型中的收益分布
Return distributions in dog-flea model revisited
摘要：
最近对相干噪声模型的研究给出了雪崩尺寸分布指数$τ$与适合于模型返回分布的$q$ -高斯分布的$q$值之间的精确关系。将这种关系应用于埃克塞特的历史狗蚤模型，将热平衡附近的波动视为雪崩。我们提供了一个清晰的数值证据，当系统尺寸足够大时，涨落长度分布的指数$τ$与合适的$q$ -Gaussian的$q$值之间的关系服从这个精确的关系。这使我们能够确定的$q$ -参数\emph{a priori}的值，从一个众所周知的指数，这样的动力系统。此外，研究还表明，随着系统规模的增大，狗蚤模型的收益率分布逐渐趋于$q$ -高斯分布，这种趋势可以用一个定义良好的解析表达式来分析.
英文摘要：
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 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 appropriate $q$-Gaussian obeys this exact relation when the system size is large enough. This allows us to determine the value of $q$-parameter \emph{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 to $q$-Gaussian as the system size increases and this tendency can be analyzed by a well defined analytical expression.
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