Jack Deformations of Plancherel Measures and Traceless Gaussian Random Matrices
Jack Deformations of Plancherel Measures and Traceless Gaussian Random Matrices
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 …