Duality and evolving set bounds on mixing times

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.

References in corpus (3)

• The Evolution of the Mixing Rate
• The simple random walk and max-degree walk on a directed graph
• Intersection conductance and canonical alternating paths, methods for general finite Markov chains

Cited by in corpus (1)

• Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements