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

Jaime Garza and Yizao Wang

Stochastic Processes and their Applications, 2025, vol. 188, issue C

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 Dn,j denoting the number of urns with j-balls after the first n samplings, ∑j=1najDn,j for a prescribed sequence of real numbers (aj)j∈N. The main applications are limit theorems for random permutations induced by Chinese restaurant processes with (α,θ)-seating with α∈(0,1),θ>−α. An example is briefly mentioned here, and full details are provided in an accompanying paper.

Date: 2025
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DOI: 10.1016/j.spa.2025.104665

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