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.
Citation
Ravi Montenegro. "Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels." Electron. Commun. Probab. 12 377 - 389, 2007. https://doi.org/10.1214/ECP.v12-1269
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