Spectrum and combinatorics of two-dimensional Ramanujan complexes

Konstantin Golubev*, Ori Parzanchevski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageAmerican English
Pages (from-to)583-612
Number of pages30
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - 1 Mar 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019, The Hebrew University of Jerusalem.


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