Successive maxima of samples from a GEM distribution
  We show that the maximal value in a size $n$ sample from GEM$(\theta)$ distribution is distributed as a sum of independent geometric random variables. This implies that the maximal value grows as $\theta\log(n)$ as $n\to\infty$. For the two-parametric GEM$(\alpha,\theta)$ distribution we show that the maximal value grows as a random factor of $n^{\alpha/(1-\alpha)}$ and find the limiting distribution. 
Jim Pitman and Yuri Yakubovich
math.PR