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

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 Laplacia...

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Bibliographic Details
Published inDiscrete & computational geometry Vol. 59; no. 2; pp. 293 - 330
Main Author Oppenheim, Izhar
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2018
Springer Nature B.V
Subjects
Combinatorics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Spectra
Graph Laplacian
Spectral gap
Secondary 05A20
05C81
High dimensional expanders
Simplicial complexes
Primary 05E45
Online AccessGet full text
ISSN0179-5376
1432-0444
DOI10.1007/s00454-017-9948-x

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Summary: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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SourceType-Scholarly Journals-1
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content type line 14
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-017-9948-x