Random unitaries in non-commutative tori, and an asymptotic model for q-circular systems

TL;DR

This paper studies q-circular systems, a deformation of free probability constructs, demonstrating that averages of random unitaries in non-commutative tori asymptotically resemble these systems, linking random matrix models to non-commutative probability.

Contribution

It introduces an asymptotic model for q-circular systems using random unitaries in non-commutative tori, expanding the understanding of deformations in free probability.

Findings

Averages of random unitaries in non-commutative tori behave asymptotically like q-circular systems.

The work establishes a connection between random matrix models and q-deformed free probability.

Provides a new framework for studying deformations of free probability systems.

Abstract

We consider the concept of a q-circular system, which is a deformation of the circular system from free probability, taking place in the framework of the so-called 'q-commutation relations'. We show that certain averages of random unitaries in non-commutative tori behave asymptotically like a q-circular system.