Spectrum and combinatorics of two-dimensional Ramanujan complexes
Combinatorics
2019-06-03 v3 Representation Theory
Spectral Theory
Abstract
Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high dimensional Hodge-Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudo-randomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.
Cite
@article{arxiv.1406.6666,
title = {Spectrum and combinatorics of two-dimensional Ramanujan complexes},
author = {Konstantin Golubev and Ori Parzanchevski},
journal= {arXiv preprint arXiv:1406.6666},
year = {2019}
}