The Gaussian beta-ensemble is one of the classical model in random matrix theory. It generalizes the eigenvalue process of the Gaussian orthogonal/unitary ensembles at an arbitrary temperature and it can be realized as the eigenvalue process of a random tridiagonal matrix with independent entries [Dumitriu-Edelman]. In particular, this model gives a probabilistic coupling which is relevant to study the asymptotics of the characteristic polynomials of these tridiagonal matrices as the matrix dimension tends to infinity. I will report on joint works with Elliot Paquette (McGill University) where we relate these asymptotics to “classical objects” in random matrix theory, such as the Sine and Airy point processes, as well as a Gaussian log-correlated field. One can view our results as a stochastic counterpart of the classical Plancherel-Rotach asymptotics for the Hermite polynomials (β = ∞).