Limit theorems for random permutations induced by Chinese restaurant processes
| Autor: | Garza, Jaime, Wang, Yizao |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We investigate the random permutation matrices induced by the Chinese restaurant processes with $(\alpha,\theta)$-seating. When $\alpha=0,\theta>0$, the permutations are those following Ewens measures on symmetric groups, and have been extensively studied in the literature. Here, we consider $\alpha\in(0,1)$ and $\theta>-\alpha$. In an accompanying paper, a functional central limit theorem is established for partial sum of weighted cycle counts in the form of $\sum_{j=1}^n a_jC_{n,j}$, where $C_{n,j}$ is the number of $j$-cycles of the permutation matrix of size $n$. Two applications are presented. One is on linear statistics of the spectrum, and the other is on the characteristic polynomials outside the unit circle. Comment: 17 pages |
| Databáze: | arXiv |
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