Stochastic aspects of easy quantum groups

TL;DR

This paper investigates the stochastic properties of certain easy quantum groups, analyzing the asymptotic behavior of trace powers of their fundamental representations, and connects these results to classical groups like O_n and S_n.

Contribution

It extends the analysis of asymptotic laws of trace functions to specific orthogonal quantum groups satisfying easiness, generalizing known classical results.

Findings

Asymptotic laws of Tr(u^k) computed for various quantum groups

Connections established between quantum and classical group trace distributions

Generalization of classical results by Diaconis and Shahshahani

Abstract

We consider several orthogonal quantum groups satisfying the easiness assumption axiomatized in our previous paper. For each of them we discuss the computation of the asymptotic law of Tr(u^k) with respect to the Haar measure, u being the fundamental representation. For the classical groups O_n, S_n we recover in this way some well-known results of Diaconis and Shahshahani.