Doob equivalence and non-commutative peaking for Markov chains

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Doob equivalence and non-commutative peaking for Markov chains. / Chen, Xinxin; Dor-On, Adam; Hui, Langwen; Linden, Christopher; Zhang, Yifan.

In: Journal of Noncommutative Geometry, Vol. 15, No. 4, 2021, p. 1469-1484.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Chen, X, Dor-On, A, Hui, L, Linden, C & Zhang, Y 2021, 'Doob equivalence and non-commutative peaking for Markov chains', Journal of Noncommutative Geometry, vol. 15, no. 4, pp. 1469-1484. https://doi.org/10.4171/JNCG/444

APA

Chen, X., Dor-On, A., Hui, L., Linden, C., & Zhang, Y. (2021). Doob equivalence and non-commutative peaking for Markov chains. Journal of Noncommutative Geometry, 15(4), 1469-1484. https://doi.org/10.4171/JNCG/444

Vancouver

Chen X, Dor-On A, Hui L, Linden C, Zhang Y. Doob equivalence and non-commutative peaking for Markov chains. Journal of Noncommutative Geometry. 2021;15(4):1469-1484. https://doi.org/10.4171/JNCG/444

Author

Chen, Xinxin ; Dor-On, Adam ; Hui, Langwen ; Linden, Christopher ; Zhang, Yifan. / Doob equivalence and non-commutative peaking for Markov chains. In: Journal of Noncommutative Geometry. 2021 ; Vol. 15, No. 4. pp. 1469-1484.

Bibtex

@article{4a498555153e49d3a150ecf99bc65f0f,
title = "Doob equivalence and non-commutative peaking for Markov chains",
abstract = "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.",
keywords = "Doob equivalence, Harmonic functions, Liouville property, Non-commutative peaking, Rigidity, Stochastic matrices, Tensor algebras",
author = "Xinxin Chen and Adam Dor-On and Langwen Hui and Christopher Linden and Yifan Zhang",
note = "Publisher Copyright: {\textcopyright} 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license",
year = "2021",
doi = "10.4171/JNCG/444",
language = "English",
volume = "15",
pages = "1469--1484",
journal = "Journal of Noncommutative Geometry",
issn = "1661-6952",
publisher = "European Mathematical Society Publishing House",
number = "4",

}

RIS

TY - JOUR

T1 - Doob equivalence and non-commutative peaking for Markov chains

AU - Chen, Xinxin

AU - Dor-On, Adam

AU - Hui, Langwen

AU - Linden, Christopher

AU - Zhang, Yifan

N1 - Publisher Copyright: © 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Doob equivalence

KW - Harmonic functions

KW - Liouville property

KW - Non-commutative peaking

KW - Rigidity

KW - Stochastic matrices

KW - Tensor algebras

U2 - 10.4171/JNCG/444

DO - 10.4171/JNCG/444

M3 - Journal article

AN - SCOPUS:85123782504

VL - 15

SP - 1469

EP - 1484

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 4

ER -

ID: 297058510