Local spectral expansion approach to high dimensional expanders part I:\n Descent of spectral gaps

2017/09/13 by Izhar Oppenheim, Oppenheim, Izhar
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Molecular spectroscopy and chirality #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1709.04431

openalex publication_date 2017/09/13 · 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\ncomplex as a possible analogue of spectral expansion defined for graphs. We\nthen show that the condition of local spectral expansion for a complex yields\nvarious spectral gaps in both the links of the complex and the global\nLaplacians of the complex.\n

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