Abstract
It is well-known in percolation theory (and intuitively plausible) that two events of the form “there is an open path from s to a ”are positively correlated. We prove the (not intuitively obvious) fact that this is still true if we condition on an event of the form “there is no open path from s to t.”
Citation
J. Kahn. J. van den Berg. "A correlation inequality for connection events in percolation." Ann. Probab. 29 (1) 123 - 126, February 2001. https://doi.org/10.1214/aop/1008956324
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