A correlation inequality for connection events in percolation

@inproceedings{Berg1999ACI,
title={A correlation inequality for connection events in percolation},
author={Jacob van den Berg and Jonas Kahn},
year={1999}
}

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”. 1991 Mathematics Subject Classification: 05C99 60C05 60K35.