Israel Journal of Mathematics

, Volume 230, Issue 2, pp 583–612 | Cite as

Spectrum and combinatorics of two-dimensional Ramanujan complexes

  • Konstantin GolubevEmail author
  • Ori Parzanchevski


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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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsThe Hebrew University of Jerusalem Givat RamJerusalemIsrael
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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