From Ramanujan Graphs to Ramanujan Complexes
Number Theory
2019-12-12 v1 Combinatorics
Representation Theory
Abstract
Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high dimensional theory has emerged. In this paper these developments are surveyed. After explaining their connection to the Ramanujan conjecture we will present some old and new results with an emphasis on random walks on these discrete objects and on the Euclidean spheres. The latter lead to "golden gates" which are of importance in quantum computation.
Cite
@article{arxiv.1904.03533,
title = {From Ramanujan Graphs to Ramanujan Complexes},
author = {Alexander Lubotzky and Ori Parzanchevski},
journal= {arXiv preprint arXiv:1904.03533},
year = {2019}
}
Comments
To appear in the proceedings of the Ramanujan Centenary Celebration at the Royal Society