Probability distributions over energy and areas in processes described by Kolmogorov's 1934 random motion equation

The Kolmogorov equation is described in detail in the paper by G.S. Golitsyn [Phys. Usp. 67 80 (2024); Usp. Fiz. Nauk 194 86 (2024)], which is a summary of the book by G.S. Golitsyn, Probability structures of the macrocosm: earthquakes, hurricanes, floods (Moscow: Fizmatlit, 2022), but insufficient attention is paid to probability distributions, integral and differential, for the processes described by this equation. The integral distribution for cosmic rays is derived only by the method of similarity and dimensionality, and the distribution of horizontal lengths L of clouds and their perimeters together with the ratio of the cloud perimeter to its size are not explained at all. Here, these shortcomings are corrected, and the results and methods can be useful for other purposes.

Keywords: distribution function, random motions, second moments of probability distribution, statistical laws of nature
PACS: 05.40.−a, 91.30.−f, 96.50.S− (all)
DOI: 10.3367/UFNe.2025.08.039983
URL: https://ufn.ru/en/articles/2025/9/g/
Web of Science

001606315700007
Scopus

2-s2.0-105021830975
ADS NASA

2025PhyU...68..954G
Citation: Golitsyn G S "Probability distributions over energy and areas in processes described by Kolmogorov's 1934 random motion equation" Phys. Usp. 68 954–956 (2025)

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Received: 29th, November 2024, revised: 31st, July 2025, accepted: 1st, August 2025

Оригинал: Голицын Г С «Распределение вероятностей по энергии и площадям в процессах, описываемых уравнением случайных движений Колмогорова 1934 года» УФН 195 1017–1019 (2025); DOI: 10.3367/UFNr.2025.08.039983

References (14) ↓ Similar articles (3)

Golitsyn G S Phys. Usp. 67 80 (2024); Golitsyn G S Usp. Fiz. Nauk 194 86 (2024)
Golitsyn G S Veroyatnostnye Struktury Makromira: Zemletryaseniya, Uragany, Navodneniya... (Probability Structures Of The Macrocosm: Earthquakes, Hurricanes, Floods...) (Moscow: Fizmatlit, 2022)
Obukhov A M Advances In Geophysics Vol. 6 (Eds H E Landsberg, J Van Mieghem) (New York: Academic Press, 1959) p. 113
Feller W An Introduction To Probability Theory And Its Applications (New York: Wiley, 1970, 1971); Translated into Russian, Feller W Vvedenie V Teoriyu Veroyatnostei I Ee Prilozheniya (Moscow: Mir, 1967)
Newman M E J Contemp. Phys. 46 323 (2005)
Karelin A V et al J. Exp. Theor. Phys. 119 448 (2014); Karelin A V et al Zh. Eksp. Teor. Fiz. 146 513 (2014)
Berezinskii V S et al Astrophysics Of Cosmic Rays (Ed. V L Ginzburg) (Amsterdam: North-Holland, 1990); Translated from Russian, Berezinskii V S et al Astrofizika Kosmicheskikh Luchei (Ed. V L Ginzburg) 2nd ed. (Moscow: Nauka, 1990)
Mandelbrot B B Fractals: Form, Chance, And Dimension (San Francisco: W. H. Freeman, 1977)
Lovejoy S Science 216 185 (1982)
von Savigny C et al Geophys. Res. Lett. 38 L02806 (2011)
Golitsyn G S, Chkhetiani O G, Vazaeva N V Izv. Atmos. Ocean. Phys. 58 645 (2022)
Golitsyn G S, Chkhetiani O G, Vazaeva N V Izv. Ross. Akad. Nauk Fiz. Atmos. Okeana 59 242 (2023)
Chernokul’skii A V, Mokhov I I Issled. Zemli Kosmosa (3) 12 (2010)
Bird P Geochem. Geophys. Geosyst. 4 1027 (2003)