On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs
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...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/140575 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862667743068684288 |
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| author | Khorunzhiy, O. |
| author_facet | Khorunzhiy, O. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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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| first_indexed | 2025-12-07T15:23:53Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-140575 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T15:23:53Z |
| publishDate | 2017 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Khorunzhiy, O. 2018-07-10T19:26:47Z 2018-07-10T19:26:47Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/140575 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs Article published earlier |
| spellingShingle | On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs Khorunzhiy, O. |
| title | On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs |
| title_full | On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs |
| title_fullStr | On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs |
| title_full_unstemmed | On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs |
| title_short | On Eigenvalue Distribution of Random Matrices of Ihara Zeta Function of Large Random Graphs |
| title_sort | on eigenvalue distribution of random matrices of ihara zeta function of large random graphs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/140575 |
| work_keys_str_mv | AT khorunzhiyo oneigenvaluedistributionofrandommatricesofiharazetafunctionoflargerandomgraphs |