Exponential moments of block-size probabilities decide when union-of-random-blocks processes on Z^d are finitary factors of IID and when they are stochastically dominated by non-trivial Bernoulli percolation.
A characterization of those processes finitarily isomorphic to a Bernoulli shift
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Finitary codings and stochastic domination for Poisson representable processes
Exponential moments of block-size probabilities decide when union-of-random-blocks processes on Z^d are finitary factors of IID and when they are stochastically dominated by non-trivial Bernoulli percolation.