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Random eigenvalues of graphenes and the triangulation of plane
Journal of Physics A: Mathematical and Theoretical. 2025. Vol. 58. No. 2. Article 025212.
We analyze the numbers of closed paths of length on two important regular lattices: the hexagonal lattice (also called graphene in chemistry) and its dual triangular lattice. These numbers form a moment sequence of specific random variables connected to the distance of a position of a planar random flight (in three steps) from the origin. Here, we refer to such a random variable as a random eigenvalue of the underlying lattice. Explicit formulas for the probability density and characteristic functions of these random eigenvalues are given for both the hexagonal and the triangular lattice. Furthermore, it is proven that both probability distributions can be approximated by a functional of the random variable uniformly distributed on increasing intervals as . This yields a straightforward method to simulate these random eigenvalues without generating graphene and triangular lattice graphs. To demonstrate this approximation, we first prove a key integral identity for a specific series containing the third powers of the modified Bessel functions In nth order, . Such series play a crucial role in various contexts, in particular, in analysis, combinatorics, and theoretical physics.
Keywords: combinatoricstheoretical physicsModified Bessel functionhexagonal latticedual triangular lattice.
Publication based on the results of:
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Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84
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Chertopolokhov V., Mukhamedov A., Bugriy G. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
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Морозов С. В., Calcolo 2026 Vol. 63 No. 2 Article 23
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Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 Article 18
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Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 Article 106192
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Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
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Gurevich E., Saraev I., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 19–56
In this paper, we consider a class of gradient-like ows without heteroclinic
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Added: May 15, 2026
Aleskerov F. T., Khutorskaya O., Stepochkina A. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
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Dorovskiy A., / Series arXiv "math". 2026.
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Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
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Springer, 2025.
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Khestanov R., Suvalko A., Социологическое обозрение 2025 Т. 24 № 2 С. 164–189
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Added: March 5, 2025
Уфа: Издательство БГПУ, 2023.
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