Weighing the "heaviest" Polya urn

For the classical Polya urn model parametrized by exponent gamma, the limit distributions of the fraction of balls in each bin are simple and well known when gamma < 1 ("egalitarian") and when gamma > 1 ("winner takes all"). In this note, we partially fill in the gap for gamma = 1, the critical point, by providing explicit analytical expressions for all the moments of the limit distribution of the fraction of balls in the bin with the most balls. (C) 2014 Elsevier B.V. All rights reserved.