Spectral gap bounds for the simplicial Laplacian and an application to random complexes
Article Type
Research Article
Publication Title
Journal of Combinatorial Theory. Series A
Abstract
In this article, we derive two spectral gap bounds for the reduced Laplacian of a general simplicial complex. Our two bounds are proven by comparing a simplicial complex in two different ways with a larger complex and with the corresponding clique complex respectively. Both of these bounds generalize the result of Aharoni et al. (2005) [1] which is valid only for clique complexes. As an application, we investigate the thresholds for vanishing of cohomology of the neighborhood complex of the Erdös-Rényi random graph. We improve the upper bound derived in Kahle (2007) [12] by a logarithmic factor using our spectral gap bounds and we also improve the lower bound via finer probabilistic estimates than those in Kahle (2007) [12].
DOI
10.1016/j.jcta.2019.105134
Publication Date
1-1-2020
Recommended Citation
Shukla, Samir and Yogeshwaran, D., "Spectral gap bounds for the simplicial Laplacian and an application to random complexes" (2020). Journal Articles. 546.
https://digitalcommons.isical.ac.in/journal-articles/546
Comments
Open Access, Green