Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues

@inproceedings{ErdHos2016FluctuationsOR,
  title={Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues},
  author={L'aszl'o ErdHos and Dominik Schr{\"o}der},
  year={2016}
}
We prove a new CLT for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor Ĥ and find that the fluctuation is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of H and Ĥ. In particular our theorem identifies the fluctuation of Kerov’s rectangular Young diagrams, defined by the interlacing eigenvalues of H and Ĥ, around their asymptotic shape, the Vershik-Kerov-Logan… Expand

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