Eliazar Iddo
Holon Institute of Technology, P.O. Box 305, Holon 58102, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):052125. doi: 10.1103/PhysRevE.87.052125. Epub 2013 May 20.
This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
本文对由指数强度和幂律强度控制的泊松过程进行了全面的“重整化研究”。这些泊松过程至关重要，因为它们构成了贡贝尔、弗雷歇和韦布尔通用极值定律的基石。应用泊松重整化方法，我们分析了这些泊松过程的出现，揭示了它们的内在动力学结构，确定了它们的吸引域，并刻画了它们的结构相变。结果表明，这些结构相变受均匀强度与调和强度的控制，具有通用的吸引域，独特地展现出内在不变性，并且与“白噪声”和“1/f噪声”密切相关。因此，我们为白噪声和1/f噪声的普遍存在建立了一种泊松解释。
