TY - GEN

T1 - Construction of new local spectral high dimensional expanders

AU - Kaufman, Tali

AU - Oppenheim, Izhar

N1 - Publisher Copyright:
© 2018 Association for Computing Machinery.

PY - 2018/6/20

Y1 - 2018/6/20

N2 - 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.

AB - 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.

KW - High dimensional expanders

KW - Simplicial complexes

KW - Spectral gap

UR - http://www.scopus.com/inward/record.url?scp=85049889203&partnerID=8YFLogxK

U2 - 10.1145/3188745.3188782

DO - 10.1145/3188745.3188782

M3 - Conference contribution

AN - SCOPUS:85049889203

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 952

EP - 963

BT - STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

A2 - Henzinger, Monika

A2 - Kempe, David

A2 - Diakonikolas, Ilias

PB - Association for Computing Machinery

T2 - 50th Annual ACM Symposium on Theory of Computing, STOC 2018

Y2 - 25 June 2018 through 29 June 2018

ER -