Doob equivalence and non-commutative peaking for Markov chains
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In this paper, we show how questions about operator algebras constructed from stochastic matrices motivate new results in the study of harmonic functions on Markov chains. More precisely, we characterize the coincidence of conditional probabilities in terms of (generalized) Doob transforms, which then leads to a stronger classification result for the associated operator algebras in terms of spectral radius and strong Liouville property. Furthermore, we characterize the noncommutative peak points of the associated operator algebra in a way that allows one to determine them from inspecting the matrix. This leads to a concrete analogue of the maximum modulus principle for computing the norm of operators in the ampliated operator algebras.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Journal of Noncommutative Geometry |
| Vol/bind | 15 |
| Udgave nummer | 4 |
| Sider (fra-til) | 1469-1484 |
| Antal sider | 16 |
| ISSN | 1661-6952 |
| DOI | |
| Status | Udgivet - 2021 |
Bibliografisk note
Funding Information:
Funding. This project supported by NSF grant DMS-1449269. Research of the second author supported by NSF grant DMS-1900916 and by the European Union’s Horizon 2020 Marie Sklodowska-Curie grant 839412. Research of the fourth author supported by the Campus Research Board Award RB 19110.
Funding Information:
This project supported by NSF grant DMS-1449269. Research of the second author supported by NSF grant DMS-1900916 and by the European Union's Horizon 2020 Marie Sklodowska-Curie grant 839412. Research of the fourth author supported by the Campus Research Board Award RB 19110.
Publisher Copyright:
© 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license
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