Affiliation:
1. Dipartimento Ingegneria Chimica Materiali Ambiente, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
Abstract
The Central Limit Theorem stands as a milestone in probability theory and statistical physics, as the privileged, if not the unique, universal route to normal distributions. This article addresses and describes several other alternative routes to Gaussianity, stemming from physical interactions, related to particle-particle and radiative particle–photon elementary processes. The concept of conservative mixing transformations of random ensembles is addressed, as it represents the other main universal distributional route to Gaussianity in classical low-energy physics. Monadic ensemble transformations are introduced, accounting for radiative particle–photon interactions, and are intimately connected with the theory of random Iterated Function Systems. For Monadic transformations, possessing a thermodynamic constraint, Gaussianity represents the equilibrium condition in two limiting cases: in the low radiative-friction limit in any space dimension, and in the high radiative-friction limit, when the dimension of the physical space tends to infinity.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference65 articles.
1. Gnedenko, B.V., and Kolmogorov, A.N. (1954). Limit Distributions for Sums of Independent Random Variables, Addison-Wesley.
2. Petrov, V.V. (1975). Sums of Independent Random Variables, Springer.
3. Lévy, P. (1925). Calcul dés Probabilités, Gautier-Villars.
4. Zolotarev, V.M. (1986). One-Dimensional Stable Distributions, American Mathematical Society.
5. Kac, M. (2018). Statistical Independence in Probability, Analysis & Number Theory, Dover Publications.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献