Abstract
The investigation of spectral properties of random block-hierarchical matrices as applied to dynamic and structural characteristics of complex hierarchical systems with disorder is proposed for the first time. Peculiarities of dynamics on random ultrametric energy landscapes are discussed and the statistical properties of scale-free and polyscale (depending on the topological characteristics under investigation) random hierarchical networks (graphs) obtained by multiple mapping are considered.
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Original Russian Text © V.A. Avetisov, A.Kh. Bikulov, O.A. Vasilyev, S.K. Nechaev, A.V. Chertovich, 2009, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 136, No. 3, pp. 566–588.
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Avetisov, V.A., Bikulov, A.K., Vasilyev, O.A. et al. Some physical applications of random hierarchical matrices. J. Exp. Theor. Phys. 109, 485–504 (2009). https://doi.org/10.1134/S1063776109090155
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DOI: https://doi.org/10.1134/S1063776109090155