Representations of Cuntz algebras associated to quasi-invariant Markov measures

Abstract

In this paper, we answer the question of equivalence, or singularity, of two given quasi-stationary Markov measures on one-sided infinite words, and the corresponding question of equivalence of associated Cuntz algebra ${Ø}_N$ representations. We do this by associating certain monic representations of ${Ø}_N$ to quasi-stationary Markov measures, and then proving that equivalence for pairs of measures is decided by unitary equivalence of the corresponding pair of representations.

References in corpus (2)

• Martingales, endomorphisms, and covariant systems of operators in Hilbert space
• Universal fermionization of bosons on permutative representations of the Cuntz algebra ${\mathcal{O}}_2$