Geodesic
Spontaneous clustering in Markov chains. III.~Monte Carlo Algorithms
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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 3, Tome 222 (2023), pp. 115-133.

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The third (final) part of the review on the modeling of spontaneous clustering of correlated point sets based on the statistics of nodes of Markov chains. Dedicated to the computational aspects of this problem, it contains a brief introduction into the method of statistical modeling (Monte Carlo method) and a detailed presentation of the specifics of its application to the problem under consideration, including solving the Ornstein-Zernike equation with the Levy-Feldheim stable kernel. The necessary information from the theory of non-Gaussian stable distributions is given, an algorithm for modeling 3-dimensional vectors with a symmetric stable distribution is described, its justification is given, accompanied by graphical and tabular material. In conclusion, the test results are presented. The first part of this work: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 220. — P. 125–144. The second part of this work: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 221. — P. 128–147.
Keywords: cumulative distribution function, inverse functions, rejection method, statistical weight, characteristic functions, Levy-stable density, functionals, approximating, testing. 
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V. V. Uchaikin; E. V. Kozhemyakina. Spontaneous clustering in Markov chains. III.~Monte Carlo Algorithms. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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 3, Tome 222 (2023), pp. 115-133. http://geodesic.mathdoc.fr/item/INTO_2023_222_a10/

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