Limit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials

$N$-dimensional Bessel and Jacobi processes describe interacting particle systems with $N$ particles are related to $\beta$-Hermite, $\beta$-Laguerre, $\beta$-Jacobi ensembles. For fixed there exist associated weak limit theorems (WLTs) in the freezing regime $\beta\to\infty$ $\beta$-Hermite $\beta$-Laguerre case by Dumitriu Edelman (2005) explicit formulas for covariance matrices $\Sigma_N$ terms of zeros orthogonal polynomials. Recently, authors derived these WLTs a different way computed $\Sigma_N^{-1}$ eigenvalues eigenvectors thus $\Sigma_N$. In present paper we use data theory finite dual polynomials de Boor Saff derive from where, ensembles, our simpler than those Edelman. We asymptotic results soft edge $N\to\infty$ Airy function. expressions