Vertex and edge expansion properties for rapid mixing
Probability
2009-04-03 v1
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).
Keywords
Cite
@article{arxiv.math/0410545,
title = {Vertex and edge expansion properties for rapid mixing},
author = {Ravi Montenegro},
journal= {arXiv preprint arXiv:math/0410545},
year = {2009}
}