A functional central limit theorem for weighted occupancy processes of the Karlin model

Abstract

A functional central limit theorem is established for weighted occupancy processes of the Karlin model. The weighted occupancy processes take the form of, with $D_{n,j}$ denoting the number of urns with $j$-balls after the first $n$ samplings, ${\sum }_{j=1}^n{a}_j{D}_{n,j}$ for a prescribed sequence of real numbers $(a_j{)}_{j\in \mathbb{N}}$. The main applications are limit theorems for random permutations induced by Chinese restaurant processes with $(\hat{I}\pm ,\hat{I}¸)$-seating with $\hat{I}\pm \in (0,1),\hat{I}¸>-\hat{I}\pm$. An example is briefly mentioned here, and full details are provided in an accompanying paper.

33 pages; accepted version