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首页> 外文期刊>Journal of Mathematical Physics, Analysis, Geometry >Fluctuations of Interlacing Sequences
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Fluctuations of Interlacing Sequences

机译：隔行序列的波动

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In a series of works published in the 1990s, Kerov put forth various applications of the circle of ideas centered at the Markov moment problem to the limiting shape of random continual diagrams arising in representation theory and spectral theory. We demonstrate on several examples that his approach is also adequate to study the fluctuations about the limiting shape. In the random matrix setting, we compare two continual diagrams: one is constructed from the eigenvalues of the matrix and the critical points of its characteristic polynomial, whereas the second one is constructed from the eigenvalues of the matrix and those of its principal submatrix. The fluctuations of the latter diagram were recently studied by Erd}os and Schr?der; we discuss the uctuations of the former, and compare the two limiting processes. For Plancherel random partitions, the Markov correspondence establishes the equivalence between Kerov's central limit theorem for the Young diagram and the Ivanov-Olshanski central limit theorem for the transition measure. We outline a combinatorial proof of the latter, and compare the limiting process with the ones of random matrices.
机译：在1990年代发表的一系列著作中，克洛夫提出了以马尔可夫矩问题为中心的思想界对在表示论和谱论中产生的随机连续图的极限形状的各种应用。我们通过几个例子证明，他的方法也足以研究极限形状的波动。在随机矩阵设置中，我们比较了两个连续图：一个是从矩阵的特征值及其特征多项式的临界点构造的，而第二个是从矩阵及其主要子矩阵的特征值构造的。最近的图的波动是由Erd} os和Schr？der研究的。我们讨论前者的求和法，并比较两个限制过程。对于Plancherel随机分区，马尔可夫对应关系在杨氏图的Kerov中心极限定理与过渡测度的Ivanov-Olshanski中心极限定理之间建立了等价关系。我们概述了后者的组合证明，并将限制过程与随机矩阵进行了比较。

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