On Convergence of Moments for Random Young Tableaux and a Random Growth Model

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.