Local Spectral Expansion Approach to High Dimensional Expanders Part I: Descent of Spectral Gaps

Izhar Oppenheim

doi:10.1007/s00454-017-9948-x

Local Spectral Expansion Approach to High Dimensional Expanders Part I: Descent of Spectral Gaps

Izhar Oppenheim

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

We introduce the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the condition of local spectral expansion for a complex yields various spectral gaps in both the links of the complex and the global Laplacians of the complex.

Original language	American English
Pages (from-to)	293-330
Number of pages	38
Journal	Discrete and Computational Geometry
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/s00454-017-9948-x
State	Published - 1 Mar 2018

Keywords

Graph Laplacian
High dimensional expanders
Simplicial complexes
Spectral gap

ASJC Scopus subject areas

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

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10.1007/s00454-017-9948-x

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title = "Local Spectral Expansion Approach to High Dimensional Expanders Part I: Descent of Spectral Gaps",

abstract = "We introduce the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the condition of local spectral expansion for a complex yields various spectral gaps in both the links of the complex and the global Laplacians of the complex.",

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author = "Izhar Oppenheim",

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KW - Graph Laplacian

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KW - Simplicial complexes

KW - Spectral gap

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Local Spectral Expansion Approach to High Dimensional Expanders Part I: Descent of Spectral Gaps

Abstract

Keywords

ASJC Scopus subject areas

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