Evolving sets , mixing and heat kernel bounds

  title={Evolving sets , mixing and heat kernel bounds},
  author={Ben Morris and Yuval Peres},
We show that a new probabilistic technique, recently introduced by the first author, yields the sharpest bounds obtained to date on mixing times of Markov chains in terms of isoperimetric properties of the state space (also known as conductance bounds or Cheeger inequalities). We prove that the bounds for mixing time in total variation obtained by Lovász and Kannan, can be refined to apply to the maximum relative deviation |pn(x, y)/π(y) − 1| of the distribution at time n from the stationary… CONTINUE READING
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