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摘要翻译：
研究了由于数据集的有限大小(FS)引起的极值极限分布的收敛性和形状修正问题。介绍了独立同分布(iid)变量的重整化方法，表明根据FS收敛指数细分iid普适类，从而确定了前序FS形状修正函数。我们发现，对于亚临界渗流和1/f^alpha平稳(alpha<1)噪声的关联系统，iid形状校正比模拟结果更好。此外，对于1/f^α噪声的强相关区(alpha>1),根据极限分布本身得到了形状校正。
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英文标题：
《Finite-size scaling in extreme statistics》
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作者：
G. Gyorgyi, N. R. Moloney, K. Ozogany, Z. Racz (Eotvos University)
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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：
We study the convergence and shape correction to the limit distributions of extreme values due to the finite size (FS) of data sets. A renormalization method is introduced for the case of independent, identically distributed (iid) variables, showing that the iid universality classes are subdivided according to the exponent of the FS convergence, which determines the leading order FS shape correction function as well. We find that, for the correlated systems of subcritical percolation and 1/f^alpha stationary (alpha<1) noise, the iid shape correction compares favorably to simulations. Furthermore, for the strongly correlated regime (alpha>1) of 1/f^alpha noise, the shape correction is obtained in terms of the limit distribution itself.
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PDF链接：
https://arxiv.org/pdf/712.3993
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