Vertex and edge expansion properties for rapid mixing

Details Vertex and edge expansion properties for rapid mixing Vertex and edge expansion properties for rapid mixing

2004-10-26

arxiv.org/abs/math/0410545v1

Random Structures & Algorithms, volume 26:1-2, pp. 52-68, 2005

Mathematics

Probability

Scientific paper

10.1002/rsa.20045

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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