HDX Condensers

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.