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Eigenvalue Ratios of Non-Negatively Curved Graphs

Published online by Cambridge University Press:  23 May 2018

SHIPING LIU
Affiliation:
Wu Wen-Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui Province, China (e-mail: spliu@ustc.edu.cn)
NORBERT PEYERIMHOFF
Affiliation:
Department of Mathematical Sciences, Durham University, DH1 3LE Durham, UK (e-mail: norbert.peyerimhoff@durham.ac.uk)
Corresponding

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.

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Paper
Copyright
Copyright © Cambridge University Press 2018 

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