Deformed Fourier models with formal parameters

TL;DR

This paper introduces a new approach to studying deformed Fourier matrices using formal parameters and analytic methods, providing insights into their algebraic structure and asymptotic behavior.

Contribution

It offers an alternative perspective on deformed Fourier matrices by replacing generic parameters with formal ones and applying analytic techniques.

Findings

Main character law is asymptotically free Poisson.

Provides an algebraic and analytic framework for deformed Fourier matrices.

Enhances understanding of fiber structures in matrix models.

Abstract

The deformed Fourier matrices $H=F_M\otimes_QF_N$, 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.