Consider a Wishart matrix X with eigenvalues λi, originating from an m × m matrix M whose entries are Gaussian with mean 0 and variance 1. That is, . Let λ 1 be the largest eigenvalue of X. Define Define τ by which normalizes L,L′ by the Johnstone normalization of Equation 7 with μ and σ defined as in Equations 5 and 6. Then L and L′ both tend in distribution to the Tracy–Widom distribution as m,n → ∞,n/m → γ > 1. That is, the normalization of Equation 28 does not change the asymptotic distribution of L.
