Spontaneous clustering in Markov chains. III. Monte Carlo Algorithms

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.