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摘要翻译：
本文回顾了关于特殊相关（或q独立）变量和的中心极限定理的最新推广，重点是q大于或等于1。具体地说，这种关联将熵Sq最大化时出现的概率密度函数q-高斯函数变成概率空间中的吸引子。此外，我们还讨论了a-稳定Levy分布的一个q-推广，它对这类特殊的关联也是稳定的。在此背景下，我们证明了一个三重熵指数的出现，它与吸引子的形式、关联和标度率有关，类似于将反常系统中表征初始条件敏感性、稳态和弛豫到稳态的熵指数联系起来的q-三重熵指数。
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英文标题：
《Nonextensive statistical mechanics and central limit theorems II -
Convolution of q-independent random variables》
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作者：
Silvio M. Duarte Queiros, Constantino Tsallis
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the probability density function known as q-Gaussian, which emerges upon maximisation of the entropy Sq, into an attractor in probability space. Moreover, we also discuss a q-generalisation of a-stable Levy distributions which can as well be stable for this special kind of correlation.Within this context, we verify the emergence of a triplet of entropic indices which relate the form of the attractor, the correlation, and the scaling rate, similar to the q-triplet that connects the entropic indices characterising the sensitivity to initial conditions, the stationary state, and relaxation to the stationary state in anomalous systems.
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PDF链接：
https://arxiv.org/pdf/709.4661
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