Percolation, first-passage percolation and covering times for Richardson's model on the \(n\)-cube (Q687712)

The authors study edge-passage percolation for the cube \(\{0,1\}^ n\) with nearest neighbour edges. They show that the critical probability is \(p=e/n\) in the oriented and \(p=1/n\) in the unoriented case. Furthermore it is shown for oriented first-passage percolation with i.i.d. passage times having a density being equal to 1 near the origin that the time to reach the opposite corner of the cube tends to 1 in probability as \(n\to\infty\). The authors also show how their results apply to the contact process with no recoveries (Richardson's model).