Heat Kernel Estimates and Homogenization for Asymptotically Lower Dimensional Processes on Some Nested Fractals

Keywords

Sierpinski triangle, Mathematics, Dirichlet form, Fractal, Diffusion process

References

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• Upper bounds for symmetric Markov transition functionsEric A. Carlen, Seiichiro Kusuoka, D. W. Stroock — 1986
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• Brownian motion on a random recursive Sierpinski gasketBen Hambly — 1997
• Transition density estimates for Brownian motion on affine nested fractalsPat Fitzsimmons, Ben Hambly, Takashi Kumagai — 1994
• Asymptotically one-dimensional diffusions on the Sierpinski gasket and theabc-gasketsKumiko Hattori, Tetsuya Hattori, Hiroshi Watanabe — 1994
• Homogenization on nested fractalsTakashi Kumagai, Seiichiro Kusuoka — 1996
• Harmonic Calculus on Limits of Networks and Its Application to DendritesJun Kigami — 1995
• T. Kato, Perturbation theory for linear operators. (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band 132) XX + 592 S. m. 3 Fig. Berlin/Heidelberg/New York Springer-Verlag. Preis geb. DM 79,20Philipp Müller — 1967
• Transition densities for Brownian motion on the Sierpinski carpetMartin T. Barlow, Richard F. Bass — 1992
• Weak Homogenization of Anisotropic Diffusion on Pre-Sierpiński CarpetsMartin T. Barlow, Kumiko Hattori, Hiroshi Watanabe — 1997
• Harmonic calculus on p.c.f. self-similar setsJun Kigami — 1993
• Waves on fractal-like manifolds and effective energy propagationShigeo Kusuoka, Xian Yin Zhou — 1998
• Harmonization and homogenization on fractalsС. М. Козлов — 1993
• Brownian motion on a homogeneous random fractalBen Hambly — 1992
• Asymptotically One-Dimensional Diffusions on Scale-Irregular GasketsTetsuya Hattori — 1997
• Brownian Motion On Nested FractalsTom Lindstrøm — 1990
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Cited by

• Asymptotically One-Dimensional Diffusion on the Sierpinski Gasket and Multi-Type Branching Processes with Varying EnvironmentBen Hambly, Owen D. Jones — 2002
• Modelling transport in disordered media via diffusion on fractalsBen Hambly, Owen D. Jones — 2000
• Anisotropic random walks and asymptotically one-dimensional diffusion onabc-gasketsTetsuya Hattori, Hiroshi Watanabe — 1997
• Periodic homogenization with an interface: The one-dimensional caseMartin Hairer, Charles Manson — 2009
• The homogenization problem for the Vicsek setBen Hambly, Volker Metz — 1998
• Asymptotically One-Dimensional Diffusions on Scale-Irregular GasketsTetsuya Hattori — 1997
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self‐Similar FractalsBen Hambly, Takashi Kumagai — 1999
• Description of diffusive and propagative behavior on fractals.Daniel Campos, Vicenç Méndez, Joaquim Fort — 2004
• Degenerate limits for one-parameter families of non-fixed-point diffusions on fractalsBen Hambly, Weiye Yang — 2016
• Dirichlet forms and critical exponents on fractalsQingsong Gu, Ka‐Sing Lau — 2017
• On a recursive construction of Dirichlet form on the Sierpiński gasketQingsong Gu, Ka‐Sing Lau, Hua Qiu — 2017
• Periodic homogenization with an interface: The multi-dimensional caseMartin Hairer, Charles Manson — 2009
• Weyl asymptotics for Hanoi attractorsPatricia Alonso Ruiz, Uta Freiberg — 2013
• Homogeneous Dirichlet Forms on p.c.f. Fractals and their Spectral AsymptoticsQingsong Gu, Ka‐Sing Lau, Hua Qiu — 2022
• Convergence, optimization and stability of singular eigenmapsBernard Akwei, Β. Τ. Sue Atkins, Rachel Bailey — 2024
• Diffusions on fractalsM. Barlow — 1998
• TRANSLATION INVARIANT DIRICHLET FORMS AND THEIR SPECTRAL ASYMPTOTICS ON P.C.F. FRACTALSKa-Sing Lau, H. Qiu — 2019

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• Brownian motion on the Sierpinski gasketMartin T. Barlow, Edwin Perkins — 1988
• Stochastic area for Brownian motion on the Sierpinski gasketBen Hambly, Terry Lyons — 1998
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• On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systemsJosé Luís da Silva, Yuri Kondratiev, Michael Röckner — 1999
• Volume doubling measures and heat kernel estimates on self-similar sets淳 木上 — 2009
• Volume Doubling Measures and Heat Kernel Estimates on Self-Similar SetsJun Kigami — 2009
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