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.
Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers.Bernoulli, pages 842–872, 2018
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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.