  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.
