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

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/s00454-017-9948-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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KW - Spectral gap

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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