摘要翻译:
充分强相关的随机变量的和在极限n\to\infty内一般不是高斯分布的。我们重新讨论了最近作为服从q-高斯定律的变量的实例而提出的和x的例子,即(cst)\乘[1-(1-q)x^2]^{1/(1-q)}型之一。我们通过显式计算表明,这些例子中的概率分布实际上在解析上不同于q-高斯分布,尽管它们在数值上非常相似。尽管q-高斯分布具有许多有趣的性质,但所研究的例子并不支持它们作为相关和的极限分布起特殊作用的观点。
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英文标题:
《A note on q-Gaussians and non-Gaussians in statistical mechanics》
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作者:
H. J. Hilhorst, G. Schehr
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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:
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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PDF链接:
https://arxiv.org/pdf/705.06