Local spectral expansion approach to high dimensional expanders

2014/07/31 by Izhar Oppenheim, Oppenheim, Izhar · 6 citations
Economics, Econometrics and Finance · Mathematics · #05A20 #05C81 #05E45 #Combinatorics (math.CO) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1407.8517

openalex publication_date 2014/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We show the condition of local spectral expansion has several nice implications. For example, for a simplicial complex with local spectral expansion we show vanishing of cohomology with real coefficients, Cheeger type inequalities and mixing type results and geometric overlap results.

Citations

• Higher Dimensional Discrete Cheeger Inequalities

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