Eigenvalue distribution of large random covariance matrices
The Marchenko–Pastur law describes the limiting spectral density of the sample covariance matrix (1/n)XᵀX for an n×p matrix X with i.i.d. entries of variance σ². As n,p→∞ with p/n→λ, eigenvalues concentrate between λ± = σ²(1±√λ)². This distinguishes signal from noise in PCA and finance.