  In recent work of Baik, Deift and Rains convergence of moments was
established for the limiting joint distribution of the lengths of the first k
rows in random Young tableaux. The main difficulty was obtaining a good
estimate for the tail of the distribution and this was accomplished through a
highly nontrival Riemann-Hilbert analysis. Here we give a simpler derivation.
The same method is used to establish convergence of moments for a random growth
model.
