  We place ourselves in the setting of high-dimensional statistical inference,
where the number of variables $p$ in a data set of interest is of the same
order of magnitude as the number of observations $n$. More formally, we study
the asymptotic properties of correlation and covariance matrices, in the
setting where $p/n\to\rho\in(0,\infty),$ for general population covariance. We
show that, for a large class of models studied in random matrix theory,
spectral properties of large-dimensional correlation matrices are similar to
those of large-dimensional covarance matrices. We also derive a
Mar\u{c}enko--Pastur-type system of equations for the limiting spectral
distribution of covariance matrices computed from data with elliptical
distributions and generalizations of this family. The motivation for this study
comes partly from the possible relevance of such distributional assumptions to
problems in econometrics and portfolio optimization, as well as robustness
questions for certain classical random matrix results. A mathematical theme of
the paper is the important use we make of concentration inequalities.
