On the recurrence of edge-reinforced random walk on Z x G

Let G be a finite tree. It is shown that edge-reinforced random walk on Z×G with large initial weights is recurrent. This includes recurrence on multi-level ladders of arbitrary width. For edge-reinforced random walk on {0,1, . . . ,n}×G, it is proved that asymptotically, with high probability, the normalized edge local times decay exponentially in the distance from the starting level. The estimates are uniform in n. They are used in the recurrence proof.