对于大于或小于典型值的罕见值，大偏差中的非对称标度
Asymmetric scaling in large deviations for rare values bigger or smaller than the typical value
摘要：
在各种无序系统或非平衡动力学模型中，某些观测量的大偏差对于大于或小于典型值的罕见值表现出不同的标度性。在本文中，我们重新审视了基于独立随机变量的简单观测量，即经验最大值，经验平均值，经验非整数矩或其他附加的经验观测量，以描述的情况下，不对称的大偏差已经发生。分析这些不同经验观测值的大偏差的统一起点由经验直方图的大偏差的Sanov定理给出：速率函数对应于相对于真实概率分布的相对熵，并且可以在存在适当约束的情况下进行优化。最后，从重整化的角度讨论了大偏差率函数的物理意义。
英文摘要：
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we revisit the simpler observables based on independent random variables, namely the empirical maximum, the empirical average, the empirical non-integer moments or other additive empirical observables, in order to describe the cases where asymmetric large deviations already occur. The unifying starting point to analyze the large deviations of these various empirical observables is given by the Sanov theorem for the large deviations of the empirical histogram : the rate function corresponds to the relative entropy with respect to the true probability distribution and it can be optimized in the presence of the appropriate constraints. Finally, the physical meaning of large deviations rate functions is discussed from the renormalization perspective.
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