  The problem of the form of the `arctic' curve of the six-vertex model with
domain wall boundary conditions in its disordered regime is addressed. It is
well-known that in the scaling limit the model exhibits phase-separation, with
regions of order and disorder sharply separated by a smooth curve, called the
arctic curve. To find this curve, we study a multiple integral representation
for the emptiness formation probability, a correlation function devised to
detect spatial transition from order to disorder. We conjecture that the arctic
curve, for arbitrary choice of the vertex weights, can be characterized by the
condition of condensation of almost all roots of the corresponding saddle-point
equations at the same, known, value. In explicit calculations we restrict to
the disordered regime for which we have been able to compute the scaling limit
of certain generating function entering the saddle-point equations. The arctic
curve is obtained in parametric form and appears to be a non-algebraic curve in
general; it turns into an algebraic one in the so-called root-of-unity cases.
The arctic curve is also discussed in application to the limit shape of
$q$-enumerated (with $0<q\leq 4$) large alternating sign matrices. In
particular, as $q\to 0$ the limit shape tends to a nontrivial limiting curve,
given by a relatively simple equation.
