Eigenvalue ratios of non-negatively curved graphs

Liu, Shiping; Peyerimhoff, Norbert

Abstract

We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality CD(0, ∞). This estimate is independent of the size of the graph and provides a general method to obtain higher-order spectral estimates. The operation of taking Cartesian products is shown to be an efficient way for constructing new weighted graphs satisfying CD(0, ∞). We also discuss a higher-order Cheeger constant-ratio estimate and related topics about expanders.

Citation

Liu, S., & Peyerimhoff, N. (2018). Eigenvalue ratios of non-negatively curved graphs. Combinatorics, Probability and Computing, 27(5), 829-850. https://doi.org/10.1017/s0963548318000214

• Journal Article Type: Article
• Acceptance Date: Mar 6, 2018
• Online Publication Date: May 23, 2018
• Publication Date: Sep 30, 2018
• Deposit Date: May 1, 2018
• Publicly Available Date: Nov 23, 2018
• Journal: Combinatorics, Probability and Computing
• Print ISSN: 0963-5483
• Electronic ISSN: 1469-2163
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 5
• Pages: 829-850
• DOI: https://doi.org/10.1017/s0963548318000214
• Public URL: https://durham-repository.worktribe.com/output/1332134