A short note on strong convergence of q-Gaussians

Abstract

In this paper, we prove strong convergence of [Formula: see text]-Gaussians with respect to a parameter [Formula: see text], which implies the spectrum of any self-adjoint non-commutative polynomial in [Formula: see text]-Gaussians is continuously deformed with respect to [Formula: see text]. With Bożejko’s Haagerup-type inequality, we follow Brannan’s approach to proving the asymptotic strong convergence of the free orthogonal quantum group.