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

Izhar Oppenheim

doi:10.1007/s00454-019-00117-7

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

Izhar Oppenheim

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Pages (from-to)	1023-1066
Number of pages	44
Journal	Discrete and Computational Geometry
Volume	64
Issue number	3
DOIs	https://doi.org/10.1007/s00454-019-00117-7
State	Published - 1 Oct 2020

Keywords

Geometrical overlapping
High dimensional expanders
Mixing
Simplicial complexes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-019-00117-7

Cite this

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title = "Local Spectral Expansion Approach to High Dimensional Expanders Part II: Mixing and Geometrical Overlapping",

abstract = "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.",

keywords = "Geometrical overlapping, High dimensional expanders, Mixing, Simplicial complexes",

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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