Representations of Cuntz algebras associated to random walks on graphs

TL;DR

This paper introduces a new class of representations of the Cuntz algebra linked to random walks on graphs, using dilation theory, and analyzes their algebraic properties.

Contribution

It presents a novel construction of Cuntz algebra representations based on graph random walks and dilation theory, expanding the understanding of their structure.

Findings

Characterization of the commutant of the representations

Analysis of intertwining operators between representations

New connections between random walks on graphs and operator algebras

Abstract

Motivated by the harmonic analysis of self-affine measures, we introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row coisometries. We study these representations, their commutant and the intertwining operators.