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Let $\boldsymbol{\Sigma}_N$ be a $M \times N$ random matrix defined by$\boldsymbol{\Sigma}_N = \mathbf{B}_N + \sigma \mathbf{W}_N$ where$\mathbf{B}_N$ is a uniformly bounded deterministic matrix and where$\mathbf{W}_N$ is an independent identically distributed complex Gaussianmatrix with zero mean and variance $\frac{1}{N}$ entries. The purpose of thispaper is to study the almost sure location of the eigenvalues$\hat{\lambda}_{1,N} \geq ... \geq \hat{\lambda}_{M,N}$ of the Gram matrix${\boldsymbol \Sigma}_N {\boldsymbol \Sigma}_N^*$ when $M$ and $N$ converge to$+\infty$ such that the ratio $c_N = \frac{M}{N}$ converges towards a constant$c > 0$. The results are used in order to derive, using an alernative approach,known results concerning the behaviour of the largest eigenvalues of${\boldsymbol \Sigma}_N {\boldsymbol \Sigma}_N^*$ when the rank of$\mathbf{B}_N$ remains fixed when $M$ and $N$ converge to $+\infty$.

Almost sure localization of the eigenvalues in a gaussian information plus noise model. Applications to the spiked models