From Ramanujan graphs to Ramanujan complexes

Alexander Lubotzky*, Ori Parzanchevski

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

4 Scopus citations


Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high-dimensional theory has emerged. In this paper, these developments are surveyed. After explaining their connection to the Ramanujan conjecture, we will present some old and new results with an emphasis on random walks on these discrete objects and on the Euclidean spheres. The latter lead to 'golden gates' which are of importance in quantum computation.

Original languageAmerican English
Article number20180445
JournalPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences
Issue number2163
StatePublished - 24 Jan 2020

Bibliographical note

Publisher Copyright:
© 2019 The Author(s) Published by the Royal Society.


  • Complexes
  • Graphs
  • Ramanujan


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