For a spectrally negative Lévy process X, killed according to a rate that is a function ω of its position, we complement the recent findings of [12] by analysing (in greater generality) the exit ...

Let 0 < a < b < ∞, and for each edge e of Zd let ω e=a or ω e=b, each with probability 1/2, independently. This induces a random metric distω on the vertices of Zd, called first passage percolation.