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 数学进展 - 2016, Vol. 45(6): 861-898
 “纪念《数学进展》创刊六十周年”特约综述文章
 随机整数划分的概率分析 Probabilistic Analysis for Random Integer Partitions 苏中根 SU Zhonggen 浙江大学数学科学学院, 杭州, 浙江, 310027 School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, 310027, P. R. China 收稿日期: 2015-01-01 出版日期: 2016-11-10 2016, Vol. 45(6): 861-898 DOI: 10.11845/sxjz.2015004a
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Abstract：Let $n\ge 1$ be a natural number. An integer partition of $n$ is by definition a sequence of natural numbers $\lambda_1,\lambda_2, \cdots, \lambda_l$ ($l\ge 1$) such that $\lambda_1+\lambda_2+\cdots+\lambda_l=n$. Let ${\mathcal P}_n$ be the set of all integer partitions of $n$, ${\mathcal P}$ the set of all integer partitions. One can produce a probability space by assigning a probability to each partition $\lambda$. There are a few of interesting probability measures worthy of consideration, among which are uniform probability measure, Plancherel measure and multiplicative measure. It turns out that it is filled with a lot of nice probability limit theorems in the study of random integer partitions. In this survey we briefly review some remarkable results including limit shapes and fluctuations of a typical random partition. For sake of clarity and conciseness, we mainly concentrate on uniform integer partitions and Plancherel partitions, and the focus is upon the use of conditioning argument in both models. We omit the proofs of most results, which can be found in original articles.
 PACS: O211
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