In this paper, we study the spectra of regular hypergraphs following the definitions from Feng and Li (1996). Our main result is an analog of Alon's conjecture for the spectral gap of the random regular hypergraphs. We then relate the second eigenvalues to both its expansion property and the mixing rate of the non-backtracking random walk on regular hypergraphs. We also prove the spectral gap for the non-backtracking operator of a random regular hypergraph introduced in Angelini et al. (2015). Finally, we obtain the convergence of the empirical spectral distribution (ESD) for random regular hypergraphs in different regimes. Under certain conditions, we can show a local law for the ESD.
@article{10_37236_8741,
author = {Ioana Dumitriu and Yizhe Zhu},
title = {Spectra of random regular hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {3},
doi = {10.37236/8741},
zbl = {1510.05180},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8741/}
}
TY - JOUR
AU - Ioana Dumitriu
AU - Yizhe Zhu
TI - Spectra of random regular hypergraphs
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8741/
DO - 10.37236/8741
ID - 10_37236_8741
ER -
%0 Journal Article
%A Ioana Dumitriu
%A Yizhe Zhu
%T Spectra of random regular hypergraphs
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8741/
%R 10.37236/8741
%F 10_37236_8741
Ioana Dumitriu; Yizhe Zhu. Spectra of random regular hypergraphs. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/8741
