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Vertex and edge expansion properties for rapid mixing

Ravi Montenegro
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Abstract

We show a strict hierarchy among various edge and vertex expansion properties of Markov chains. This gives easy proofs of a range of bounds, both classical and new, on chi-square distance, spectral gap and mixing time. The 2-gradient is then used to give an isoperimetric proof that a random walk on the grid [k]^n mixes in time O*(k^2 n).

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Ravi Montenegro. 2004-10-26. Vertex and edge expansion properties for rapid mixing. https://doi.org/10.1002/rsa.20045

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