关于图的非回退路径矩阵的极限定理
组合数学
2024-07-24 v3 数论
摘要
我们给出了关于正则图的非回退路径相关矩阵的一个极限定理。所得极限与反正弦律的第 阶矩极为相似。此外，我们得到了由 A. Lubotzky、R. Phillips 和 P. Sarnak 定义的 Ramanujan 图相关的尖形式(cusp forms)的 阶 Fourier 系数的平均值渐近式。
关键词
引用
@article{arxiv.2005.09341,
title = {The limit theorem with respect to the matrices on non-backtracking paths of a graph},
author = {Takehiro Hasegawa and Takashi Komatsu and Norio Konno and Hayato Saigo and Seiken Saito and Iwao Sato and Shingo Sugiyama},
journal= {arXiv preprint arXiv:2005.09341},
year = {2024}
}
备注
The draft is improved: Typos are fixed, Corollaries 4.3 and 4.5 are improved, and Proposition 4.6 and Remark 4.7 are added