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

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  • Garza, Jaime
  • Wang, Yizao

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.

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  • Garza, Jaime & Wang, Yizao, 2025. "A functional central limit theorem for weighted occupancy processes of the Karlin model," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001061
    DOI: 10.1016/j.spa.2025.104665
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    References listed on IDEAS

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    1. Zuopeng Fu & Yizao Wang, 2020. "Stable Processes with Stationary Increments Parameterized by Metric Spaces," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1737-1754, September.
    2. Iksanov, Alexander & Kotelnikova, Valeriya, 2022. "Small counts in nested Karlin’s occupancy scheme generated by discrete Weibull-like distributions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 283-320.
    3. Chebunin, Mikhail & Kovalevskii, Artyom, 2016. "Functional central limit theorems for certain statistics in an infinite urn scheme," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 344-348.
    4. Mikhail Chebunin & Sergei Zuyev, 2022. "Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models," Journal of Theoretical Probability, Springer, vol. 35(1), pages 1-19, March.
    5. Valentin Bahier & Joseph Najnudel, 2022. "On Smooth Mesoscopic Linear Statistics of the Eigenvalues of Random Permutation Matrices," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1640-1661, September.
    6. Durieu, Olivier & Samorodnitsky, Gennady & Wang, Yizao, 2020. "From infinite urn schemes to self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2471-2487.
    7. Bahier, Valentin, 2019. "Characteristic polynomials of modified permutation matrices at microscopic scale," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4335-4365.
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