It is now frequent that "scientists" have to deal with datasets where the sample size and the number of variables are both very large ("big data"), which strongly differs from the traditional asymptotic regime of multivariate statistics. In that respect, results from Random Matrix Theory (RMT) have found many applications in high-dimensional statistics.

After reviewing the basics of RMT for statistical inference, I will motivate the notion of anisotropic global law for the resolvent of two particular perturbation models: the free additive and the free multiplicative noise. This anisotropic law allows us to state precise results concerning the problem of estimating the "true" signal from noisy observations.

I will illustrate some of the results on the Markowitz "optimal" portfolio theory where the covariance matrix plays a crucial role, especially when the number of assets is of the same order than the sample size.