Exit time tails from pairwise decorrelation in hidden Markov chains, with applications to dynamical percolation (Q456217)

Reversible Markov processes are investigated with a focus on the relationship between the pairwise correlation of a specific event and the decay rate of a the probability of a continual occurrence of the event. It is shown that the pair-wise decorrelation of the event implies a decay of the occurrence probability. The result is quantified. Examples are provided to indicate that the results are often sharp, the non-sharpness cases are exemplified as well. The main application area is the dynamical critical percolation on planar lattices.