Eliazar Iddo
Holon Institute of Technology, P. O. Box 305, Holon 58102, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Sep;86(3 Pt 1):031103. doi: 10.1103/PhysRevE.86.031103. Epub 2012 Sep 4.
Weibull's distribution is the principal phenomenological law of relaxation in the physical sciences and spans three different relaxation regimes: subexponential ("stretched exponential"), exponential, and superexponential. The probabilistic theory of extreme-value statistics asserts that the linear scaling limits of minima of ensembles of positive-valued random variables, which are independent and identically distributed, are universally governed by Weibull's distribution. However, this probabilistic theory does not take into account spatial geometry, which often plays a key role in the physical sciences. In this paper we present a general and versatile model of random reactions in random environments and establish a geometry-based theory for the universal emergence of Weibull's distribution.
威布尔分布是物理科学中弛豫的主要唯象定律，涵盖三种不同的弛豫机制：亚指数（“拉伸指数”）、指数和超指数。极值统计的概率理论断言，独立同分布的正值随机变量集合最小值的线性缩放极限普遍受威布尔分布支配。然而，该概率理论未考虑空间几何，而空间几何在物理科学中往往起着关键作用。在本文中，我们提出了一个随机环境中随机反应的通用模型，并建立了基于几何的威布尔分布普遍出现的理论。
