Martin boundary and exit space on the Sierpinski gasket

DOI10.1007/s11425-011-4339-xzbMath1241.31014OpenAlexW1986324537MaRDI QIDQ424296

Ka-Sing Lau, Sze-Man Ngai

Publication date: 31 May 2012

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-011-4339-x

zbMATH Keywords

Martin boundaryharmonic functionMarkov chainGreen functionSierpinski gasketfractal

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Martin boundary theory (31C35) Fractals (28A80) Boundary theory for Markov processes (60J50)

Related Items (7)

Boundary theory on the Hata tree ⋮ Denker–Sato type Markov chains and Harnack inequality ⋮ Random walks and induced Dirichlet forms on self-similar sets ⋮ Noncommutative Boundaries Arising in Dynamics and Representations of the Cuntz Relations ⋮ The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain ⋮ The Role of Transfer Operators and Shifts in the Study of Fractals: Encoding-Models, Analysis and Geometry, Commutative and Non-commutative ⋮ Denker-Sato type Markov chains on self-similar sets

Cites Work

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• The construction of Brownian motion on the Sierpinski carpet
• The difference between letters and a Martin kernel of a modulo 5 Markov chain
• The Laplacian on the Sierpinski gasket via the method of averages.
• Dirichlet forms of fractals and products of random matrices
• Brownian motion on the Sierpinski gasket
• Sierpiński gasket as a Martin boundary. II: The intrinsic metric
• Dirichlet forms and associated heat kernels on the Cantor set induced by random walks on trees
• Self-similar sets as hyperbolic boundaries
• Harmonic Calculus on P.C.F. Self-Similar Sets
• A harmonic calculus on the Sierpinski spaces
• Brownian motion on nested fractals
• Reflections on Harmonic Analysis of the Sierpiński Gasket
• Random Walks on Infinite Graphs and Groups
• Post-critically finite fractal and Martin boundary
• BOUNDARY THEORY OF MARKOV PROCESSES (THE DISCRETE CASE)
• Products of Indecomposable, Aperiodic, Stochastic Matrices
• Sierpiński gasket as a Martin boundary. I: Martin kernels

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