The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain
The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain
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DOI：
10.4171/jfg/86
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发表时间：
2017-10
影响因子：
0.8
通讯作者：
Marc Kessebohmer;Tony Samuel;K. Sender
中科院分区：
文献类型：
--
作者：
Marc Kessebohmer;Tony Samuel;K. Sender
2012年，Lau和Ngai在Denker和Sato的工作的启发下，给出了一个关于三个字母表上的有限字集合的各向同性马尔可夫链的例子，其Martin边界与Sierpinski垫片同胚。本文将Lau和Ngai的结果推广到一类非迷向马氏链。我们确定了马丁边界，并证明了最小马丁边界是马丁边界的一个真子集。此外，我们给出了调和函数集的描述。
In 2012 Lau and Ngai, motivated by the work of Denker and Sato, gave an example of an isotropic Markov chain on the set of finite words over a three letter alphabet, whose Martin boundary is homeomorphic to the Sierpinski gasket. Here, we extend the results of Lau and Ngai to a class of non-isotropic Markov chains. We determine the Martin boundary and show that the minimal Martin boundary is a proper subset of the Martin boundary. In addition, we give a description of the set of harmonic functions.