title: Poissonian renormalizations, exponentials, and power laws.
abstract: 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.
authors.affiliation: Holon Institute of Technology, P.O. Box 305, Holon 58102, Israel. eliazar@post.tau.ac.il
authors.forename: Iddo
authors.initials: I
authors.lastname: Eliazar
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D016012:Poisson Distribution