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Paper:

TR23-090 | 15th June 2023 12:17

HDX Condensers

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TR23-090
Authors: Itay Cohen, Roy Roth, Amnon Ta-Shma
Publication: 18th June 2023 08:48
Downloads: 701
Keywords: 


Abstract:

More than twenty years ago, Capalbo, Reingold, Vadhan and Wigderson gave the first (and up to date only) explicit construction of a bipartite expander with almost full combinatorial expansion. The construction incorporates zig-zag ideas together with extractor technology, and is rather complicated. We give an alternative construction that builds upon recent constructions of hyper-regular, high-dimensional expanders. The new construction is, in our opinion, simple and elegant.
Beyond demonstrating a new, surprising, and intriguing, application of high-dimensional expanders, the construction employs totally new ideas which we hope may lead to progress on the still remaining open problems in the area.



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