  We revisit the computation of the discrete version of Schramm's formula for
the loop-erased random walk derived by Kenyon. The explicit formula in terms of
the Green function relies on the use of a complex connection on a graph, for
which a line bundle Laplacian is defined. We give explicit results in the
scaling limit for the upper half-plane, the cylinder and the Moebius strip.
Schramm's formula is then extended to multiple loop-erased random walks.
