English

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}
}
R2 v1 2026-07-22T17:11:37.950Z