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Spectrum and combinatorics of two-dimensional Ramanujan complexes (1406.6666v3)
Published 25 Jun 2014 in math.CO, math.RT, and math.SP
Abstract: Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high dimensional Hodge-Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudo-randomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.
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