Blocking Conductance and Mixing in Random Walks

@article{Kannan2006BlockingCA,
  title={Blocking Conductance and Mixing in Random Walks},
  author={Ravi Kannan and L{\'a}szl{\'o} Lov{\'a}sz and Ravi Montenegro},
  journal={Combinatorics, Probability & Computing},
  year={2006},
  volume={15},
  pages={541-570}
}
The notion of conductance introduced by Jerrum and Sinclair [JS88] has been widely used to prove rapid mixing of Markov Chains. Here we introduce a bound that extends this in two directions. First, instead of measuring the conductance of the worst subset of states, we bound the mixing time by a formula that can be thought of as a weighted average of the Jerrum-Sinclair bound (where the average is taken over subsets of states with different sizes). Furthermore, instead of just the conductance… CONTINUE READING
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