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This article is cited in 3 scientific papers (total in 3 papers)
Spontaneous clustering in Markov chains. II. Mesofractal model
V. V. Uchaikin Ulyanovsk State University
Abstract:
In the second part of the review, we apply theoretical principles developed in the first part to analysing statistical characteristics of clustering the observed distribution of galaxies in the visible part of the Universe. In contrast to the standard approach to solving the dynamic problem of clustering gravitational plasma based on systems of differential equations that describe the plasma as a continuous medium, we use the Ornstein–Zernike integral equation for a system of randomly distributed points whose interaction is described by an appropriate choice of the kernel of the Ornstein–Zernike equation for the two-particle correlation function. Within the framework of this “mesofractal” model, we find a $4$-parameter representation of the spectrum of fluctuation power, which allows one to determine statistical parameters of the medium from the observed data. The first part of this work: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 220. — P. 125–144.
Keywords:
gravitation plasma, galaxies, Ornstein–Zernike equation, mesofractal model, correlations, power spectrum.
Citation:
V. V. Uchaikin, “Spontaneous clustering in Markov chains. II. Mesofractal model”, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 221, VINITI, Moscow, 2023, 128–147
Linking options:
https://www.mathnet.ru/eng/into1135 https://www.mathnet.ru/eng/into/v221/p128
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