Under a block-wise contraction condition, spectral gaps of random-scan and deterministic-scan component-wise Markov chains are simultaneously positive or zero and differ by at most polynomial factors in the number of blocks.
Bounds on the L2 spectrum for Markov chains and Markov processes: a generalization of Cheeger’s inequality.Transactions of the American mathematical society, 309(2):557–580, 1988
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Solidarity of Spectral Gaps for Component-Wise Markov Chains
Under a block-wise contraction condition, spectral gaps of random-scan and deterministic-scan component-wise Markov chains are simultaneously positive or zero and differ by at most polynomial factors in the number of blocks.