Proves cutoff at entropic time log n/h for reversible mixtures of permuted Markov chains under mild assumptions on the base chains.
A short survey of Stein's method
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abstract
Stein's method is a powerful technique for proving central limit theorems in probability theory when more straightforward approaches cannot be implemented easily. This article begins with a survey of the historical development of Stein's method and some recent advances. This is followed by a description of a "general purpose" variant of Stein's method that may be called the generalized perturbative approach, and an application of this method to minimal spanning trees. The article concludes with the descriptions of some well known open problems that may possibly be solved by the perturbative approach or some other variant of Stein's method.
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UNVERDICTED 2representative citing papers
New representations of Stein operators produce explicit weighted covariance identities that deliver sharp upper and lower covariance bounds and weighted Poincaré inequalities for univariate targets, recovering classical results as corollaries.
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Cutoff for mixtures of permuted Markov chains: reversible case
Proves cutoff at entropic time log n/h for reversible mixtures of permuted Markov chains under mild assumptions on the base chains.
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First order covariance inequalities via Stein's method
New representations of Stein operators produce explicit weighted covariance identities that deliver sharp upper and lower covariance bounds and weighted Poincaré inequalities for univariate targets, recovering classical results as corollaries.