Abstract
Abstract Powering the adjacency matrix of an expander graph results in a better expander of higher degree. In this paper we seek an analogue operation for high-dimensional (HD) expanders. We show that the naive approach to powering does not preserve HD expansion and define a new power operation, using geodesic walks on quotients of Bruhat–Tits buildings. Applying this operation results in HD expanders of higher degrees. The crux of the proof is a combinatorial study of flags of free modules over finite local rings. Their geometry describes links in the power complex, and showing that they are excellent expanders implies HD expansion for the power complex by Garland’s local-to-global technique. As an application, we use our power operation to obtain new efficient double samplers.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
