图的非回溯路径上矩阵的极限定理

Pub Date : 2022-11-15 DOI:10.1007/s00026-022-00617-z

Takehiro Hasegawa, Takashi Komatsu, Norio Konno, Hayato Saigo, Seiken Saito, Iwao Sato, Shingo Sugiyama

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引用次数: 0

摘要

我们给出了一个关于与正则图的非回溯路径相关的矩阵的极限定理。所获得的极限非常类似于正弦定律的第k个矩。此外，我们还得到了A.Lubotzky、R.Phillips和p.Sarnak定义的Ramanujan图的尖点形式的第（p^m\）个傅立叶系数的平均值的渐近性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Limit Theorem with Respect to the Matrices on Non-backtracking Paths of a Graph

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 kth 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.

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