  We review the limit shape problem for the Plancherel measure and its
generalizations found in supersymmetric gauge theory instanton count. We focus
on the measure, interpolating between the Plancherel measure and uniform
measure, a U(1) case of N=2* gauge theory. We give the formula for its limit
shape in terms of elliptic functions, generalizing the trigonometric ``arcsin''
law of Vershik-Kerov and Logan-Schepp.
