关于统计力学中q-高斯与非高斯的一个注记
A note on q-Gaussians and non-Gaussians in statistical mechanics
摘要：
充分强相关的随机变量之和一般不会在极限N \to \infty中呈高斯分布。我们重新回顾最近提出的和x的例子，它们是服从q-高斯定律的变量的例子，即（cst）\times [1-（1-q）x^2]^{1/（1-q）}类型。我们通过明确的计算表明，在例子中的概率分布实际上是分析不同的q-高斯，尽管在数值上非常相似。虽然q-高斯分布具有许多有趣的性质，但研究的例子并不支持它们作为相关和的极限分布发挥特殊作用的观点。
英文摘要：
The sum of $N$ sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N\to\infty. We revisit examples of sums x that have recently been put forward as instances of variables obeying a q-Gaussian law, that is, one of type (cst)\times[1-(1-q)x^2]^{1/(1-q)}. We show by explicit calculation that the probability distributions in the examples are actually analytically different from q-Gaussians, in spite of numerically resembling them very closely. Although q-Gaussians exhibit many interesting properties, the examples investigated do not support the idea that they play a special role as limit distributions of correlated sums.
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