@inproceedings{21e9e1f298004a7480bfd27cdd541b81,
title = "Construction of new local spectral high dimensional expanders",
abstract = "High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only known construction of bounded degree high dimensional expanders is based on Ramanujan complexes, whereas one dimensional bounded degree expanders are abundant. In this work we construct new families of bounded degree high dimensional expanders obeying the local spectral expansion property. A property that implies, geometric overlapping, fast mixing of high dimensional random walks, agreement testing and agreement expansion. The construction also yields new families of expander graphs. The construction is quite elementary and it is presented in a self contained manner; This is in contrary to the highly involved construction of the Ramanujan complexes. The construction is also strongly symmetric; The symmetry of the construction could be used, for example, to obtain good symmetric LDPC codes that were previously based on Ramanujan graphs.",
keywords = "High dimensional expanders, Simplicial complexes, Spectral gap",
author = "Tali Kaufman and Izhar Oppenheim",
note = "Publisher Copyright: {\textcopyright} 2018 Association for Computing Machinery.; 50th Annual ACM Symposium on Theory of Computing, STOC 2018 ; Conference date: 25-06-2018 Through 29-06-2018",
year = "2018",
month = jun,
day = "20",
doi = "https://doi.org/10.1145/3188745.3188782",
language = "الإنجليزيّة",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
pages = "952--963",
editor = "Monika Henzinger and David Kempe and Ilias Diakonikolas",
booktitle = "STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing",
}