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Journal of the Belarusian State University. Mathematics and Informatics, 2021, Volume 3, Pages 51–56
DOI: https://doi.org/10.33581/2520-6508-2021-3-51-56
(Mi bgumi16)
 

This article is cited in 2 scientific papers (total in 2 papers)

Discrete mathematics and Mathematical cybernetics

Random walks on cayley graphs of complex reflection groups

M. M. Vas'kovskii

Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
Full-text PDF (934 kB) Citations (2)
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Abstract: Asymptotic properties of random walks on minimal Cayley graphs of complex reflection groups are investigated. The main result of the paper is theorem on fast mixing for random walks on Cayley graphs of complex reflection groups. Particularly, bounds of diameters and isoperimetric constants, a known result on fast fixing property for expander graphs play a crucial role to obtain the main result. A constructive way to prove a special case of Babai’s conjecture on logarithmic order of diameters for complex reflection groups is proposed. Basing on estimates of diameters and Cheeger inequality, there is obtained a non-trivial lower bound for spectral gaps of minimal Cayley graphs on complex reflection groups.
Keywords: complex reflection groups; Cayley graphs; random walks; expander graphs.
Document Type: Article
UDC: 519.217.2
Language: Russian
Citation: M. M. Vas'kovskii, “Random walks on cayley graphs of complex reflection groups”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2021), 51–56
Citation in format AMSBIB
\Bibitem{Vas21}
\by M.~M.~Vas'kovskii
\paper Random walks on cayley graphs of complex reflection groups
\jour Journal of the Belarusian State University. Mathematics and Informatics
\yr 2021
\vol 3
\pages 51--56
\mathnet{http://mi.mathnet.ru/bgumi16}
\crossref{https://doi.org/10.33581/2520-6508-2021-3-51-56}
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  • This publication is cited in the following 2 articles:
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    Journal of the Belarusian State University. Mathematics and Informatics
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