Duality and evolving set bounds on mixing times

Details Duality and evolving set bounds on mixing times Duality and evolving set bounds on mixing times

2006-07-02

arxiv.org/abs/math/0607031v1

Expands on Chapter 4 of monograph "Mathematical Aspects of Mixing Times in Markov Chains" by Montenegro and Tetali, NOW Publis

Mathematics

Probability

Scientific paper

We sharpen the Evolving set methodology of Morris and Peres and extend it to study convergence in total variation, relative entropy, $L^2$ and other distances. Bounds in terms of a modified form of conductance are given which apply even for walks with no holding probability. These bounds are found to be strictly better than earlier Evolving set bounds, may be substantially better than conductance profile results derived via Spectral profile, and drastically sharpen Blocking Conductance bounds if there are no bottlenecks at small sets.

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