Sharp Edge, Vertex, and Mixed Cheeger Inequalities for Finite Markov Kernels
نویسنده
چکیده
We use the evolving set methodology of Morris and Peres to show Cheeger inequalities for bounding the spectral gap of a finite ergodic Markov kernel. This leads to sharp versions of several previous inequalities, including ones involving edge-expansion and/or vertex-expansion. A bound on the smallest eigenvalue also follows
منابع مشابه
Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels
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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تاریخ انتشار 2007