Correlation Inequality for Connection Events in Percolation. Probability,211 Networks and Algorithms

摘要

It is well-known in percolation theory (and intuitively plausible) that two211u001eevents of the form 'there is an open path from s to a' are positively correlated. 211u001eWe prove the (not intuitively obvious) fact that this is still true if we 211u001econdition on an event of the form 'there is an open path from s to t.'