  The problem of the limit shape of large alternating sign matrices (ASMs) is
addressed by studying the emptiness formation probability (EFP) in the
domain-wall six-vertex model. Assuming that the limit shape arises in
correspondence to the `condensation' of almost all solutions of the
saddle-point equations for certain multiple integral representation for EFP, a
conjectural expression for the limit shape of large ASMs is derived. The case
of 3-enumerated ASMs is also considered.
