The Tracy-Widom distribution (TW) describes the density of the largest eigenvalue of a random Hermitian matrix, when scaled and centered appropriately (depending on GOE/GUE/GSE/Wishart, etc).

In a recent manuscript of mine (non-math journal), I had casually mentioned that in finite dimensional, random Hermitian matrices, the tail that extends outside the hard upperbounds in the asymptotic densities (semicircle for GOE/GUE and Marchenko-Pastur for real/complex Wishart) is also described by TW. What I had intended was that the tail is formed by the largest eigenvalue and the density of this is still governed by TW.

However, the editor of the journal commented that TW is applicable only in the asymptotic limit. Is this true? In Johnstone's 2001 paper *"On the distribution of the largest eigenvalue in principal component analysis"*, he derives a set of scaling constants for the largest eigenvalue of real Wishart matrices that explicitly depend on the dimensionality of the matrix.

Is there a disconnect between my understanding, what the editor said and what I've read in Johnstone's paper?