Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels

Ravi Montenegro

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arXiv · math/0606167

Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels

Ravi Montenegro

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Abstract

We show how the evolving set methodology of Morris and Peres can be used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel. This leads to sharp versions of several previous Cheeger inequalities, including ones involving edge-expansion, vertex-expansion, and mixtures of both. A bound on the smallest eigenvalue also follows.

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BibTeX RIS

Ravi Montenegro. 2007-05-05. Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels. https://arxiv.org/abs/math/0606167

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