Eigenvalue distribution of random covariance matrices W = XXᵀ/n
Given X a p×n matrix with i.i.d. N(0,σ²) entries, the empirical spectral distribution of W = XXᵀ/n converges as p,n→∞ with λ=p/n fixed to the Marchenko-Pastur law: ρ(λ) = (1/2πσ²λλ)√((λ+-λ)(λ-λ-)), where λ± = σ²(1±√λ)2. The ratio λ=p/n controls the spectral edge.