Poisson化Plancharel测度的KMK变换的矩的精细结构
Fine structure of moments of the KMK transform of the Poissonized Plancharel measure
摘要：
当泊松化参数$N$趋于无穷大时，考虑了泊松化Plancharel测度的渐近性态.最近Moll证明了一个收敛级数展开的统计措施$μ_λ$这是Kerov-Markov-Krein变换的带号测度的角落杰克随机分区$λ$。测度$μ_λ$是令人感兴趣的，因为它在某些方面表现得像关于GUE随机矩阵的特征值的经验测度。我们证明了泊松化Plancharel的情况下，大$N$系列的时刻$μ_λ$有一个递归结构的合理表达式的生成函数的Catalan数。我们讨论了我们的结果与GUE矩的精细结构之间的相似性。
英文摘要：
We consider asymptotics behavior of Poissonized Plancharel measures as the poissonization parameter $N$ goes to infinity. Recently Moll proved a convergent series expansion for statistics of a measure $μ_λ$ which is the Kerov-Markov-Krein transform of the signed measure on corners a Jack-random partition $λ$. The measure $μ_λ$ is of interest because it behaves in some ways like the empirical measure on eigenvalues of a GUE-random matrix. We prove for the Poissonized Plancharel case that the large $N$ series for moments of $μ_λ$ have a recursive structure as rational expressions in the generating function for Catalan numbers. We discuss the analogy between our result and the fine structure of moments of the GUE.
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