The Marchenko-Pastur law describes the limiting eigenvalue distribution of sample covariance matrices $\hat{\Sigma} = \frac{1}{n} X^T X$ when $X$ has i.i.d. entries. What setup gives non-trivial eigenvalue support?

High-Dimensional Probability (Vershynin)

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The Marchenko-Pastur law describes the limiting eigenvalue distribution of sample covariance matrices \hat{Σ} = \frac{1}{n} X^{T} X when X has i.i.d. entries. What setup gives non-trivial eigenvalue support?