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This article studies the behavior of the Maronna robust scatter estimator$\hat{C}_N\in \mathbb{C}^{N\times N}$ of a sequence of observations$y_1,...,y_n$ which is composed of a $K$ dimensional signal drown in a heavytailed noise, i.e $y_i=A_N s_i+x_i$ where $A_N \in \mathbb{C}^{N\times K}$ and$x_i$ is drawn from elliptical distribution.  In particular, we prove that as the population dimension $N$, the number ofobservations $n$ and the rank of $A_N$ grow to infinity at the same pace andunder some mild assumptions, the robust scatter matrix can be characterized bya random matrix $\hat{S}_N$ that follows a standard random model. Our analysiscan be very useful for many applications of the fields of statistical inferenceand signal processing.

The random matrix regime of Maronna's M-estimator for observations corrupted by elliptical noises