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.
Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images.IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(6):721–741, 1984
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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.