物理系统中的全球波动：和与极值统计之间的微妙相互作用
Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
摘要：
全局加性量的波动，例如总能量或磁化强度，原则上可以用（可能相关的）随机变量之和的统计来描述。然而，事实证明，极值（一组随机变量中的最大值）也可能以直接或间接的方式在全局量的统计中发挥作用。这篇评论讨论了不同的连接，可能出现的问题之间的总和和极值的随机变量，并强调物理情况下，这种连接是相关的。沿着这一思路，回顾了独立同分布随机变量和与极值的标准收敛定理，并对相关或异分布随机变量给出了一些严格的结果和启发性的推论.更具体地说，广泛分布的变量的总和内的极端值的作用得到解决，并提出了一个一般的极端值和总和之间的映射，使我们能够识别一类相关的随机变量的总和如下（广义）极值分布。这一特定类别的随机变量的可能的应用说明了两个简单的物理模型的例子。一些扩展到其他相关类的随机变量共享类似的定性性质也简要讨论，在所谓的BHP分布。
英文摘要：
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest value among a set of random variables) may also play a role in the statistics of global quantities, in a direct or indirect way. This review discusses different connections that may appear between problems of sums and of extreme values of random variables, and emphasizes physical situations in which such connections are relevant. Along this line of thought, standard convergence theorems for sums and extreme values of independent and identically distributed random variables are recalled, and some rigorous results as well as more heuristic reasonings are presented for correlated or non-identically distributed random variables. More specifically, the role of extreme values within sums of broadly distributed variables is addressed, and a general mapping between extreme values and sums is presented, allowing us to identify a class of correlated random variables whose sum follows (generalized) extreme value distributions. Possible applications of this specific class of random variables are illustrated on the example of two simple physical models. A few extensions to other related classes of random variables sharing similar qualitative properties are also briefly discussed, in connection with the so-called BHP distribution.
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