Kerov's interlacing sequences and random matrices

Abstract

To a $N\times N$ real symmetric matrix Kerov assigns a piecewise linear function whose local minima are the eigenvalues of this matrix and whose local maxima are the eigenvalues of its $(N-1)\times (N-1)$ submatrix. We study the scaling limit of Kerov's piecewise linear functions for Wigner and Wishart matrices. For Wigner matrices the scaling limit is given by the Verhik-Kerov-Logan-Shepp curve which is known from asymptotic representation theory. For Wishart matrices the scaling limit is also explicitly found, and we explain its relation to the Marchenko-Pastur limit spectral law.

13 pages

References in corpus (1)

• Kerov's central limit theorem for Schur-Weyl measures of parameter 1/2

Cited by in corpus (5)

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• Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues
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• Representations of classical Lie groups and quantized free convolution
• A Quantized Analogue of the Markov-Krein Correspondence