Scaling-limit conjecture for model 1 and model 2 spectra

Let $n$ be the matrix size and let $m\leq n$ be the model parameter, with fixed parameters $\delta$ and $a$. Spectral scaling conjecture. For both model 1 and model 2, when $n$ and $m$ are sufficiently large, the sizes of the spectra and pseudospectra are determined by the ratio $m/n$. Consequently, numerical eigenvalue patterns for different pairs $(n,m)$ with the same ratio $n/m$ have components of similar sizes when both parameters are sufficiently large. Equivalently, there are nontrivial scaling limits with $n\to\infty$, $m\to\infty$, and fixed $m/n\in(0,1)$. This conjectures a ratio-controlled asymptotic regime for both spectral and pseudospectral patterns; the supplied text provides no resolution.