2019/11/23 by Xinxin Chen, Chen, Xinxin, Adam Dor-On +7
Mathematics · #47L75 #47L80. Secondary: 60J45 #60J50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Primary: 60J10 #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1911.10423
openalex publication_date 2019/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 non-commutative 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.