The limit theorem with respect to the matrices on non-backtracking paths of a graph
Combinatorics
2024-07-24 v3 Number Theory
Abstract
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 th moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the th Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak.
Keywords
Cite
@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}
}
Comments
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