A functional central limit theorem for weighted occupancy processes of the Karlin model
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909585377329152 |
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| author | Garza, Jaime Wang, Yizao |
| author_facet | Garza, Jaime Wang, Yizao |
| contents | 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, $\sum_{j=1}^na_jD_{n,j}$ 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 $(α,θ)$-seating with $α\in(0,1), θ>-α$. An example is briefly mentioned here, and full details are provided in an accompanying paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02160 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A functional central limit theorem for weighted occupancy processes of the Karlin model Garza, Jaime Wang, Yizao Probability 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, $\sum_{j=1}^na_jD_{n,j}$ 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 $(α,θ)$-seating with $α\in(0,1), θ>-α$. An example is briefly mentioned here, and full details are provided in an accompanying paper. |
| title | A functional central limit theorem for weighted occupancy processes of the Karlin model |
| topic | Probability |
| url | https://arxiv.org/abs/2412.02160 |