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arXiv · 1406.6617

Eigenvalue ratios of nonnegatively curved graphs

Shiping Liu·Norbert Peyerimhoff
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Abstract

We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality $CD(0,\infty)$. 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 $CD(0,\infty)$. We also discuss a higher order Cheeger constant ratio estimate and related topics about expanders.

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Shiping Liu, Norbert Peyerimhoff. 2014-06-25. Eigenvalue ratios of nonnegatively curved graphs. https://doi.org/10.1017/s0963548318000214

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