Eigenvalue ratios of non-negatively curved graphs

Liu, Shiping; Peyerimhoff, Norbert

doi:10.1017/s0963548318000214

Eigenvalue ratios of non-negatively curved graphs

Liu, Shiping; Peyerimhoff, Norbert

Authors

Shiping Liu

Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor

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

Files

Accepted Journal Article (398 Kb)
PDF

Copyright Statement
This article has been published in a revised form in Combinatorics, probability and computing https://doi.org/10.1017/s0963548318000214. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2018.