The Sierpi\'nski gasket as the Martin boundary of a non-isotropic Markov chain

Autor:	Tony Samuel, Karenina Sender, Marc Kesseböhmer
Jazyk:	angličtina
Rok vydání:	2017
Předmět:	Physics Mathematics::Logic 31C35 60J50 28A80 60J10 Markov chain Harmonic function Applied Mathematics Mathematical analysis Isotropy Boundary (topology) Geometry and Topology Mathematics - Dynamical Systems Mathematics - Probability Sierpinski triangle
Popis:	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 Sierpi\'nski 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. Comment: 13 pages, 5 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8476786651d7e6e3dfab9e82f1ed2f75 http://arxiv.org/abs/1710.04414 Zobrazit plný text záznamu