  In this paper, we provide a framework of estimates for describing 2D scaling
limits by Schramm's SLE curves. In particular, we show that a weak estimate on
the probability of an annulus crossing implies that a random curve arising from
a statistical mechanics model will have scaling limits and those will be
well-described by Loewner evolutions with random driving forces. Interestingly,
our proofs indicate that existence of a nondegenerate observable with a
conformally-invariant scaling limit seems sufficient to deduce the required
condition.
  Our paper serves as an important step in establishing the convergence of
Ising and FK Ising interfaces to SLE curves, moreover, the setup is adapted to
branching interface trees, conjecturally describing the full interface picture
by a collection of branching SLEs.
