Doob equivalence and non-commutative peaking for Markov chains
Doob equivalence and non-commutative peaking for Markov chains
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DOI：
10.4171/jncg/444
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发表时间：
2019-11
影响因子：
0.9
通讯作者：
Xinxin Chen;Adam Dor-On;Langwen Hui;C. Linden;Yifan Zhang
中科院分区：
文献类型：
--
作者：
Xinxin Chen;Adam Dor-On;Langwen Hui;C. Linden;Yifan Zhang
在本文中，我们将展示如何从随机矩阵构造的算子代数的问题，激发新的研究结果的调和函数的马尔可夫链。更确切地说，我们的（广义）Doob变换的条件概率的重合的特征，然后导致一个更强的分类结果的相关算子代数的谱半径和强刘维尔性质。此外，我们的特征的非交换的峰值点的相关算子代数的方式，允许一个来确定他们从检查矩阵。这导致了一个具体的模拟最大模原则计算规范的运营商在cumulated运营商代数。
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.