Another normality is possible. Distributive transformations and emergent Gaussianity

Massimiliano Giona, Chiara Pezzotti and Giuseppe Procopio

Physica A: Statistical Mechanics and its Applications, 2024, vol. 634, issue C

Abstract: A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations (CMT) in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism characterizing the application of Central Limit Theorem, as it is based on the iteration of a random transformation preserving the ensemble variance. Gaussianity emerges as a “supergeneric” property of ensemble statistics, in the case the energy constraint is quadratic in the norm of the variables. This result puts in a different light the occurrence of equilibrium Gaussian distributions in kinetic variables (velocity, momentum), as it shows mathematically that, in the absence of any other dynamic mechanisms, almost Gaussian distributions stem from the low-velocity approximations of the physical conservation principles. Whenever, the energy constraint is not expressed in terms of quadratic functions non-Gaussian distributions arise. This is case of relativistic collisional interactions where the Jüttner distribution is recovered from CMT.

Keywords: Stochastic dynamics; Normal distribution; Collisions; Jüttner distribution; Conservation principles (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437123010051
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:634:y:2024:i:c:s0378437123010051

DOI: 10.1016/j.physa.2023.129450

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().