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

Marc Kesseböhmer; Tony Samuel; Karenina Sender

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

Marc Kesseböhmer
, Tony Samuel
, Karenina Sender

Mathematics

Research output: Contribution to conference (unpublished) › Poster

55 Downloads (Pure)

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.

Original language	English
Publication status	Published - 2018
Event	Fractal Geometry and Stochastics 6 - Bad-Herrenalb, Germany Duration: 30 Sept 2018 → 5 Oct 2018

Conference

Conference	Fractal Geometry and Stochastics 6
Country/Territory	Germany
City	Bad-Herrenalb
Period	30/09/18 → 5/10/18

Access to Document

The Sierpinski gasket as the Martin boundary of a non-isotropic Markov chainFinal published version, 204 KB

Cite this

@conference{dc43363e792a4fa8b4c9e3a64d90c076,

title = "The Sierpi{\'n}ski gasket as the Martin boundary of a non–isotropic Markov chain",

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 Sierpi{\'n}ski gasket. Here, we extend the results of Lau and Ngai to a class of non-isotropic Markov chains. ",

author = "Marc Kesseb{\"o}hmer and Tony Samuel and Karenina Sender",

year = "2018",

language = "English",

note = "Fractal Geometry and Stochastics 6 ; Conference date: 30-09-2018 Through 05-10-2018",

}

TY - CONF

T1 - The Sierpiński gasket as the Martin boundary of a non–isotropic Markov chain

AU - Kesseböhmer, Marc

AU - Samuel, Tony

AU - Sender, Karenina

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

M3 - Poster

T2 - Fractal Geometry and Stochastics 6

Y2 - 30 September 2018 through 5 October 2018

ER -

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

Abstract

Conference

Access to Document

Fingerprint

Cite this