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.

Correspondence should be addressed to 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/ 001606315700007 2-s2.0-105021830975 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) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks 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