A note on the elementary construction of High-Dimensional Expanders of Kaufman and Oppenheim
Prahladh Harsha, Ramprasad Saptharishi
TL;DR
This paper provides an elementary, self-contained proof of the construction of spectral high-dimensional expanders and standard expanders, simplifying previous complex methods and making the construction more accessible.
Contribution
It offers a simplified, elementary proof of Kaufman and Oppenheim's construction of spectral high-dimensional expanders, enhancing understanding and accessibility.
Findings
Elementary proof of high-dimensional expander construction
Simplified analysis of standard expanders
Accessible approach to spectral expansion properties
Abstract
In this note, we give a self-contained and elementary proof of the elementary construction of spectral high-dimensional expanders using elementary matrices due to Kaufman and Oppenheim [Proc. 50th ACM Symp. on Theory of Computing (STOC), 2018]. As a bonus, this also yields a simple construction and analysis of standard expanders.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Matrix Theory and Algorithms · Quantum Computing Algorithms and Architecture