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Mixing under monotone censoring. (English) Zbl 1317.60087
Summary: Consider critical percolation on a rhombus in the hexagonal lattice, and let \(A\) be the event of a left to right crossing (by 1’s). Suppose we sample configurations from \(A\) by starting from some fixed configuration in \(A\), and then at each step a uniformly random hexagon is resampled as long as the resulting configuration is in \(A\). It is easy to see that this sampling procedure converges to the uniform distribution on \(A\). How long would it take? in this short note we will analyze the mixing properties of this chain and, more generally, initiate the study of mixing times of Markov chains under monotone censoring. A number of open problems are presented.

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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