Deformed Fourier models with formal parameters

The deformed Fourier matrices $H=F_M{\otimes }_Q{F}_N$, with $Q\in {\mathbb{T}}^{MN}$, produce a matrix model $C(S_{MN}^{+})\to M_{MN}(C({\mathbb{T}}^{MN}))$. When $Q\in {\mathbb{T}}^{MN}$ is generic, the corresponding fiber can be investigated via algebraic techniques, and the main character law is asymptotically free Poisson. We present here an alternative point of view on these questions, using formal parameters instead of generic parameters, and analytic tools.