Consider a N×n random matrix Zn​=(Zj1​j2​n​) where the
individual entries are a realization of a properly rescaled stationary gaussian
random field.
The purpose of this article is to study the limiting empirical distribution
of the eigenvalues of Gram random matrices such as Zn​Zn∗​ and (Zn​+An​)(Zn​+An​)∗ where An​ is a deterministic matrix with appropriate
assumptions in the case where n→∞ and nN​→c∈(0,∞).
The proof relies on related results for matrices with independent but not
identically distributed entries and substantially differs from related works in
the literature (Boutet de Monvel et al., Girko, etc.).Comment: 15 page