The limit theorem with respect to the matrices on non-backtracking paths of a graph
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866929430760259584 |
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| author | Hasegawa, Takehiro Komatsu, Takashi Konno, Norio Saigo, Hayato Saito, Seiken Sato, Iwao Sugiyama, Shingo |
| author_facet | Hasegawa, Takehiro Komatsu, Takashi Konno, Norio Saigo, Hayato Saito, Seiken Sato, Iwao Sugiyama, Shingo |
| contents | We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the $k$th moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the $p^m$th Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_09341 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The limit theorem with respect to the matrices on non-backtracking paths of a graph Hasegawa, Takehiro Komatsu, Takashi Konno, Norio Saigo, Hayato Saito, Seiken Sato, Iwao Sugiyama, Shingo Combinatorics Number Theory 05C38 (Primary), 05C50, 11F30 (Secondary) We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the $k$th moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the $p^m$th Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak. |
| title | The limit theorem with respect to the matrices on non-backtracking paths of a graph |
| topic | Combinatorics Number Theory 05C38 (Primary), 05C50, 11F30 (Secondary) |
| url | https://arxiv.org/abs/2005.09341 |