The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-10-12 DOI:10.4171/JFG/86

Marc Kessebohmer, Tony Samuel, K. Sender

引用次数: 2

Abstract

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.

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Sierpiński垫圈作为非各向同性Markov链的Martin边界

2012年，在Denker和Sato工作的推动下，Lau和Ngai给出了一个三字母字母表上有限词集上的各向同性马尔可夫链的例子，其Martin边界与Sierpinski垫圈同胚。在这里，我们将Lau和Ngai的结果推广到一类非各向同性马尔可夫链。我们确定了Martin边界，并证明了最小Martin边界是Martin边界的一个子集。此外，我们还描述了调和函数的集合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.