2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144760It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance matrix $\frac1p XX^T$, where $X$ is a $n\times p$ matrix with independent entries and the distribution function of the Marchenko-Pastur law is of order $O(n^{-1/2})$. The bounds hold {\it uniformly} for any $p$, including $\frac pn$ equal or close to 1.ProbabilitySpectral Theory60B99text