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Spectrum and combinatorics of two-dimensional Ramanujan complexes

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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 pseudorandomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.

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Authors and Affiliations

  1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, Jerusalem, 91904, Israel

    Konstantin Golubev

  2. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Ori Parzanchevski

Authors
  1. Konstantin Golubev
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  2. Ori Parzanchevski
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Correspondence to Konstantin Golubev.

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Golubev, K., Parzanchevski, O. Spectrum and combinatorics of two-dimensional Ramanujan complexes. Isr. J. Math. 230, 583–612 (2019). https://doi.org/10.1007/s11856-019-1828-z

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  • DOI: https://doi.org/10.1007/s11856-019-1828-z

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