Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels
Probability
2007-12-03 v2 Combinatorics
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.
Cite
@article{arxiv.math/0606167,
title = {Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels},
author = {Ravi Montenegro},
journal= {arXiv preprint arXiv:math/0606167},
year = {2007}
}
Comments
v1: original version (>20 pages) v2: v1 was far too verbose; this pares it to under 10 pages