  We prove that the edge-reinforced random walk on the ladder
${\mathbb{Z}\times\{1,2\}}$ with initial weights $a>3/4$ is recurrent. The
proof uses a known representation of the edge-reinforced random walk on a
finite piece of the ladder as a random walk in a random environment. This
environment is given by a marginal of a multicomponent Gibbsian process. A
transfer operator technique and entropy estimates from statistical mechanics
are used to analyze this Gibbsian process. Furthermore, we prove spatially
exponentially fast decreasing bounds for normalized local times of the
edge-reinforced random walk on a finite piece of the ladder, uniformly in the
size of the finite piece.
