Local Spectral Expansion Approach to High Dimensional Expanders Part II: Mixing and Geometrical Overlapping

  • Izhar OppenheimEmail author
Ricky Pollack memorial issue


We further explore the local-to-global approach for expansion of simplicial complexes that we call local spectral expansion. Specifically, we prove that local expansion in the links implies the global expansion phenomena of mixing and geometric overlapping. Our mixing results also give tighter bounds on the error terms compared to previously known results.


Mixing Simplicial complexes High dimensional expanders Geometrical overlapping 

Mathematics Subject Classification

Primary 05E45, Secondary 05A20 05C81 



The author would like to thank Matthew Kahle and Tali Kaufman for many useful discussions and Alexander Lubotzky for the inspiration to pursue this subject. The author was partially supported by ISF Grant No. 293/18.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsBen-Gurion University of the NegevBe’er ShevaIsrael

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