Geodesic
Random partitions growth by appending parts: power weights case
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 277-306
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We investigate a generalization of Ewens measures on integer partitions where parts of size $k$ have weights $\theta_k\ge 0$. The Ewens measure is a partial case of the constant sequence $\theta_k\equiv\theta>0$. In this paper we consider the case when partial sums $\theta_1+\dots+\theta_k$ have regular growth of index greater that $1$ as $k\to\infty$. We introduce a continuous time random partition growth process such that given it visits some partition of $n$, the random partition of $n$ it visits has the generalized Ewens distribution. In contrast to the often considered growth procedure, in which parts are increased by $1$ or a new part $1$ is added, in the growth process defined in the paper parts are added one by one and remain in the partition forever. The partition growth process is derived explicitly from a sequence of independent Poisson processes. This allows to establish strong laws of large numbers for some characteristics of the process and to determine its asymptotic behavior. 
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     author = {Yu. V. Yakubovich},
     title = {Random partitions growth by appending parts: power weights case},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {277--306},
     year = {2024},
     volume = {535},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a18/}
}
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Yu. V. Yakubovich. Random partitions growth by appending parts: power weights case. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 277-306. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a18/

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