Kerov's interlacing sequences and random matrices

Alexey Bufetov

doi:10.1063/1.4830024

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arXiv · 1211.1507

Kerov's interlacing sequences and random matrices

Alexey Bufetov

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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.

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Alexey Bufetov. 2012-11-07. Kerov's interlacing sequences and random matrices. https://doi.org/10.1063/1.4830024

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