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

2024/12/03 by Garza, Jaime, Yizao Wang, Wang, Yizao
Decision Sciences · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2412.02160

openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, ∑_j=1ⁿa_jD_n,j for a prescribed sequence of real numbers (a_j)_{j∈\mathbb 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.

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