Conservation operator processes from asymptotic representation theory and their CLT

TL;DR

This paper develops a central limit theorem for conservation operator processes within asymptotic representation theory, analyzing their behavior in large unitary and quantum groups, bridging algebraic methods and probability theory.

Contribution

It introduces a CLT for conservation operator processes and applies it to asymptotic analysis of large unitary and quantum groups.

Findings

Established a CLT for conservation operator processes.

Analyzed asymptotic behavior of processes from unitary groups.

Provided applications to quantum asymptotic representation theory.

Abstract

In this paper, we examine applications of the theory of operator-valued processes to algebraic methods in probability theory. We show a central limit theorem for general conservation operator processes. Utilizing this, we analyze the asymptotic behavior of processes derived from unitary groups and quantum unitary groups as their ranks tend to infinity, thereby providing applications of asymptotic representation theory.