Jack Deformations of Plancherel Measures and Traceless Gaussian Random Matrices
Jack Deformations of Plancherel Measures and Traceless Gaussian Random Matrices
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DOI：
10.37236/873
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发表时间：
2008-10
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影响因子：
--
通讯作者：
Sho Matsumoto
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文献类型：
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作者：
Sho Matsumoto
我们研究了$n$的长度不大于一个固定数$d$的随机分拆$\lambda=（\mada_1，\mada_2，\dots，\mada_d）$。假设一个随机划分$\lambda$是根据杰克测度分布的，这是一个变形的Plancherel测度与一个正参数$\alpha>0$。我们证明了对于所有的$\alpha>0$，在$n \to \infty$的极限下，标度$\dots，\lambda_d$的联合分布收敛于来自无痕高斯$\beta$-系综的一些随机变量的联合分布，其中$\beta=2/\alpha$.我们还给出了一个简短的证明雷格夫的渐近定理的总和$\beta$的权力$f^\lambda$，一些标准tableaux的形状$\lambda$。
We study random partitions $\lambda=(\lambda_1,\lambda_2,\dots,\lambda_d)$ of $n$ whose length is not bigger than a fixed number $d$. Suppose a random partition $\lambda$ is distributed according to the Jack measure, which is a deformation of the Plancherel measure with a positive parameter $\alpha>0$. We prove that for all $\alpha>0$, in the limit as $n \to \infty$, the joint distribution of scaled $\lambda_1,\dots, \lambda_d$ converges to the joint distribution of some random variables from a traceless Gaussian $\beta$-ensemble with $\beta=2/\alpha$. We also give a short proof of Regev's asymptotic theorem for the sum of $\beta$-powers of $f^\lambda$, the number of standard tableaux of shape $\lambda$.