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.
Exponential rates of convergence in the ergodic theorem: a constructive approach.Journal of Statistical Physics, 139(3):367–374, 2010
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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.