On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs
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| Creator |
Khorunzhiy, O.
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| Description |
We consider the ensemble of real symmetric random matrices H(n,ρ) obtained from the determinant form of the Ihara zeta function of random graphs that have n vertices with the edge probability ρ/n. We prove that the normalized eigenvalue counting function of H(n,ρ) converges weakly in average as n, ρ→∞ and ρ = o(nα) for any α > 0 to a shift of the Wigner semi-circle distribution. Our results support a conjecture that the large Erdős-Rényi random graphs satisfy in average the weak graph theory Riemann Hypothesis.
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| Date |
2018-07-10T19:26:47Z
2018-07-10T19:26:47Z 2017 |
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| Type |
Article
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| Identifier |
On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs / O. Khorunzhiy // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 3. — С. 268-282. — Бібліогр.: 27 назв. — англ.
1812-9471 DOI: doi.org/10.15407/mag13.03.268 Mathematics Subject Classification 2000: 05C50, 05C80, 15B52, 60F99 http://dspace.nbuv.gov.ua/handle/123456789/140575 |
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| Language |
en
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| Relation |
Журнал математической физики, анализа, геометрии
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| Publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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