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.
42 Then, for everyπβ (0,1), Ξ¦(π 2 Ξ π ) β₯πmin 1βπ 2 , π2π π‘ 4
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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.