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

Research output: Contribution to journalArticlepeer-review

Authors

  • Marc Kesseböhmer
  • Tony Samuel
  • Karenina Sender

Colleges, School and Institutes

External organisations

  • University of Bremen

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 Sierpiński 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.

Details

Original languageEnglish
Pages (from-to)113-136
Number of pages21
JournalJournal of Fractal Geometry
Volume7
Issue number2
Early online date19 May 2020
Publication statusE-pub ahead of print - 19 May 2020

Keywords

  • Martin boundary, Markov chain, Green function, Harmonic function, Sierpinski gasket