On the disconnection of a discrete cylinder by a biased random walk

We consider a random walk on the discrete cylinder (./N.)d.., d.3 with drift N.d. in the .-direction and investigate the large N-behavior of the disconnection time TNdisc, defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent . is strictly greater than 1, the asymptotic behavior of TNdisc remains N2d+o(1), as in the unbiased case considered by Dembo and Sznitman, whereas for .<1, the asymptotic behavior of TNdisc becomes exponential in N.