Blocking Conductance and Mixing in Random Walks

  title={Blocking Conductance and Mixing in Random Walks},
  author={Ravi Kannan and L{\'a}szl{\'o} Mikl{\'o}s Lov{\'a}sz and Ravi Montenegro},
  journal={Combinatorics, Probability and Computing},
  pages={541 - 570}
The notion of conductance introduced by Jerrum and Sinclair [8] 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… 
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