约束物理系统的极值理论
Extreme value theory for constrained physical systems
摘要：
我们研究了具有全局守恒定律的物理系统的极值理论，这些系统描述了更新过程、质量输运模型和长程相互作用自旋模型。如前所述，一个特殊的特征是极值的分布在支撑的中间显示出一个非分析点。我们暴露的约束极值理论和众所周知的数量的基础随机动力学之间的确切关系，所有有效超出中点的一般性，即，甚至远离热力学极限。例如，对于更新过程，两个更新事件之间的最大时间的分布与这些事件的平均数完全相关。在热力学极限，我们展示了我们的理论是如何适合于描述典型的和罕见的事件，偏离经典的极值理论。例如，对于更新过程，我们解开了极值分布的双重标度，指出了两种类型的限制律：典型统计量的归一化标度函数和描述罕见事件的非归一化状态。
英文摘要：
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the distribution of the extreme value exhibits a non-analytical point in the middle of the support. We expose exact relationships between constrained extreme value theory and well-known quantities of the underlying stochastic dynamics, all valid beyond the midpoint in generality, i.e. even far from the thermodynamic limit. For example for renewal processes, the distribution of the maximum time between two renewal events is exactly related to the mean number of these events. In the thermodynamic limit, we show how our theory is suitable to describe typical and rare events which deviate from classical extreme value theory. For example for the renewal process, we unravel dual scaling of the extreme value distribution, pointing out two types of limiting laws: a normalisable scaling function for the typical statistics and a non-normalised state describing the rare events.
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