A lower bound for disconnection by simple random walk (Q2412662)

The asymptotic behavior of the probability that a large body gets disconnected from infinity by the set of points visited by a simple random walk on \(\mathcal{Z}^d, d\geq 3\), was investigated in recent works and some asymptotic upper bounds were obtained. Using random interlacements in \(\mathcal{Z}^d\), i.e. Poissonian clouds of doubly-infinite nearest-neighbor paths, the author proves asymptotic lower bounds. It is reasonably conjectured that asymptotic lower and upper bounds match.