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Duality and evolving set bounds on mixing times

Ravi Montenegro
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Abstract

This survey is an in-depth development of the theoretical aspects of the method of Evolving Sets, a method which has been used in several of my papers. It is fairly esoteric as to a large degree it stems from my efforts to ascertain whether Evolving sets is provably stronger than other isoperimetric methods (answer: yes, with qualifications). For an introduction to the method please see Chapter 4 of my book "Mathematical aspects of mixing times in Markov chains" with Prasad Tetali, or the paper "Evolving sets, mixing and heat kernel bounds" by Morris and Peres.

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Ravi Montenegro. 2018-06-01. Duality and evolving set bounds on mixing times. https://arxiv.org/abs/math/0607031

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