In this talk, we will review some of the classical models of large random matrices, namely large empirical covariance matrices, of interest in many applications such as statistics, electrical engineering and data science.
Given a population covariance matrix, the associated large empirical covariance matrix can exhibit a spectrum with many interesting features such as multiple connected components, outliers (that is lonely eigenvalues outside from the main bulk), etc. Much information about the underlying data structure can be gained from a precise analysis of the matrix eigenstructure.
We will review classical and modern results on spiked models and outliers, multiple connected component spectrum. We will then present recent results on samples of stationnary observations which substantially modify the classical landscape.
Talk based on joint papers with Banna, Hachem, Hardy, MerlevĂ¨de, Tian
