Asymptotically one-dimensional diffusions on the Sierpinski gasket and the \(abc\)-gaskets

DOI10.1007/BF01204955zbMath0808.60067MaRDI QIDQ1336268

Kumiko Hattori, Hiroshi Watanabe, Tetsuya Hattori

Publication date: 12 March 1995

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

renormalization grouplimit theoremdiffusion processesSierpinski gasketdiscrete-time multi-type non-stationary branching processes

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Sums of independent random variables; random walks (60G50) Applications of branching processes (60J85) Diffusion processes (60J60) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics (82C28) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

Related Items (10)

On the convergence of multitype branching processes with varying environments ⋮ Weyl asymptotics for Hanoi attractors ⋮ On a recursive construction of Dirichlet form on the Sierpiński gasket ⋮ Homogeneous Dirichlet forms on p.c.f. fractals and their spectral asymptotics ⋮ Degenerate limits for one-parameter families of non-fixed-point diffusions on fractals ⋮ A characterization of certain diffusions on the Sierpinski gasket by the exit distributions ⋮ Dirichlet forms and critical exponents on fractals ⋮ Anisotropic random walks and asymptotically one-dimensional diffusion on \(abc\)-gaskets ⋮ On the asymptotic patterns of supercritical branching processes in varying environments ⋮ Modelling transport in disordered media via diffusion on fractals.

Cites Work

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• The construction of Brownian motion on the Sierpinski carpet
• Brownian motion on the Sierpinski gasket
• Dirichlet forms on fractals: Poincaré constant and resistance
• Self-avoiding paths on the three dimensional Sierpinski gasket
• Regularity, closedness and spectral dimensions of the Dirichlet forms on P.C.F. self-similar sets
• Estimates of transition densities for Brownian motion of nested fractals
• Self-similar diffusions on a class of infinitely ramified fractals
• Harmonic Calculus on P.C.F. Self-Similar Sets
• Brownian motion on nested fractals
• Coupling and Harnack inequalities for Sierpiński carpets

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