Extreme value theory for constrained physical systems.
Extreme value theory for constrained physical systems.
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DOI：
10.1103/physreve.102.042141
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Marc Höll;Wanli Wang;E. Barkai
中科院分区：
文献类型：
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作者：
Marc Höll;Wanli Wang;E. Barkai
我们研究极值理论的物理系统的整体守恒定律，描述更新过程，质量输运模型，和远程相互作用的自旋模型。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。我们揭示了约束极值理论和基础随机动态的众所周知的数量之间的确切关系，所有这些都在中点之外有效，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，我们解开的极值分布的双重标度，指出两种类型的限制法律：一个规范化的标度函数的典型统计和非规范化的状态描述罕见的事件。
We investigate extreme value theory for physical systems with a global conservation law which describes 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 nonanalytical 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 general, 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 normalizable scaling function for the typical statistics and a non-normalized state describing the rare events.