10.1093/imrn/rnw330
Erdös, László
László
Erdös0000-0001-5366-9603
Schröder, Dominik J
Dominik J
Schröder
Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues
Oxford University Press
2018
2018-12-11T11:49:41Z
2020-01-17T09:49:10Z
journal_article
https://research-explorer.app.ist.ac.at/record/1012
https://research-explorer.app.ist.ac.at/record/1012.json
10737928
1608.05163
We prove a new central limit theorem (CLT) for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor H 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 H. In particular, our theorem identifies the fluctuation of Kerov's rectangular Young diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel measure follow the same limiting shape. For this, algebraically motivated, ensemble a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar to our result but the variance is different, indicating that the analogy between the two models has its limitations. Moreover, our theorem shows that Borodin's result [7] on the convergence of the spectral distribution of Wigner matrices to a Gaussian free field also holds in derivative sense.