  The Generalized Chinese Restaurant Process (GCRP) describes a sequence of
exchangeable random partitions of the numbers $\{1,\dots,n\}$. This process is
related to the Ewens sampling model in Genetics and to Bayesian nonparametric
methods such as topic models. In this paper, we study the GCRP in a regime
where the number of parts grows like $n^\alpha$ with $\alpha>0$. We prove a
non-asymptotic concentration result for the number of parts of size
$k=o(n^{\alpha/(2\alpha+4)}/(\log n)^{1/(2+\alpha)})$. In particular, we show
that these random variables concentrate around $c_{k}\,V_*\,n^\alpha$ where
$V_*\,n^\alpha$ is the asymptotic number of parts and $c_k\approx
k^{-(1+\alpha)}$ is a positive value depending on $k$. We also obtain
finite-$n$ bounds for the total number of parts. Our theorems complement
asymptotic statements by Pitman and more recent results on large and moderate
deviations by Favaro, Feng and Gao.
