Martin Boundary and Exit Space on the Sierpinski Gasket and Other Fractals

Sze-Man Ngai; Ka-Sing Lau

Martin Boundary and Exit Space on the Sierpinski Gasket and Other Fractals

Sze-Man Ngai, Ka-Sing Lau

Mathematical Sciences

The Chinese University of Hong Kong

Research output: Contribution to conference › Presentation

Abstract

<div class="line" id="line-29"> We de&filig;ne a Markov chain on a discrete symbolic space corresponding to the Sierpinski gasket (SG) and show that its Martin boundary is homeomorphic to the SG, while the minimal Martin boundary can be identi&filig;ed with the three vertices of the SG. Moreover, we show that the harmonic functions coincide with the standard ones. We also consider generalizations to a larger class of p.c.f. fractals. This is a joint work with Ka-Sing Lau.</div>

Original language	American English
State	Published - Sep 10 2011
Event	Northeastern Sectional Meeting of the American Mathematical Society (AMS) - Ithaca, NY Duration: Sep 10 2011 → …

Conference

Conference	Northeastern Sectional Meeting of the American Mathematical Society (AMS)
Period	09/10/11 → …

Disciplines

Mathematics

Keywords

Karkov chain
Martin boundary
SG
Sierpinski gasket

Cite this

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title = "Martin Boundary and Exit Space on the Sierpinski Gasket and Other Fractals",

abstract = " We de&filig;ne a Markov chain on a discrete symbolic space corresponding to the Sierpinski gasket (SG) and show that its Martin boundary is homeomorphic to the SG, while the minimal Martin boundary can be identi&filig;ed with the three vertices of the SG. Moreover, we show that the harmonic functions coincide with the standard ones. We also consider generalizations to a larger class of p.c.f. fractals. This is a joint work with Ka-Sing Lau.",

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author = "Sze-Man Ngai and Ka-Sing Lau",

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note = "Northeastern Sectional Meeting of the American Mathematical Society (AMS) ; Conference date: 10-09-2011",

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TY - CONF

T1 - Martin Boundary and Exit Space on the Sierpinski Gasket and Other Fractals

AU - Ngai, Sze-Man

AU - Lau, Ka-Sing

PY - 2011/9/10

Y1 - 2011/9/10

N2 - We de&filig;ne a Markov chain on a discrete symbolic space corresponding to the Sierpinski gasket (SG) and show that its Martin boundary is homeomorphic to the SG, while the minimal Martin boundary can be identi&filig;ed with the three vertices of the SG. Moreover, we show that the harmonic functions coincide with the standard ones. We also consider generalizations to a larger class of p.c.f. fractals. This is a joint work with Ka-Sing Lau.

AB - We de&filig;ne a Markov chain on a discrete symbolic space corresponding to the Sierpinski gasket (SG) and show that its Martin boundary is homeomorphic to the SG, while the minimal Martin boundary can be identi&filig;ed with the three vertices of the SG. Moreover, we show that the harmonic functions coincide with the standard ones. We also consider generalizations to a larger class of p.c.f. fractals. This is a joint work with Ka-Sing Lau.

KW - Karkov chain

KW - Martin boundary

KW - SG

KW - Sierpinski gasket

UR - http://www.ams.org/amsmtgs/2189_abstracts/1072-31-163.pdf

M3 - Presentation

T2 - Northeastern Sectional Meeting of the American Mathematical Society (AMS)

Y2 - 10 September 2011

ER -

Martin Boundary and Exit Space on the Sierpinski Gasket and Other Fractals

Abstract

Conference

Disciplines

Keywords

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