Jack deformations of Plancherel measures and traceless Gaussian random matrices
The electronic journal of combinatorics, Tome 15 (2008)
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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 $\lambda$.
Sho Matsumoto. Jack deformations of Plancherel measures and traceless Gaussian random matrices. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/873
@article{10_37236_873,
author = {Sho Matsumoto},
title = {Jack deformations of {Plancherel} measures and traceless {Gaussian} random matrices},
journal = {The electronic journal of combinatorics},
year = {2008},
volume = {15},
doi = {10.37236/873},
zbl = {1159.60009},
url = {http://geodesic.mathdoc.fr/articles/10.37236/873/}
}
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