Asymptotics of the transition probabilities of the simple random walk on self-similar graphs

DOI10.1090/S0002-9947-03-03352-XzbMath1030.60064arXivmath/0209143MaRDI QIDQ4429752

Elmar Teufl, Bernhard Krön

Publication date: 28 September 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209143

zbMATH Keywords

Green functionssimple random walkself-similar graph

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05)

Related Items (19)

Spectral decimation of a self-similar version of almost Mathieu-type operators ⋮ Spectral zeta functions of fractals and the complex dynamics of polynomials ⋮ Enumeration problems for classes of self-similar graphs ⋮ Spectral analysis on infinite Sierpiński fractafolds ⋮ Perfect quantum state transfer on diamond fractal graphs ⋮ Weak uncertainty principle for fractals, graphs and metric measure spaces ⋮ Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs ⋮ On the spectral theory of trees with finite cone type ⋮ On-diagonal oscillation of the heat kernels on post-critically finite self-similar fractals ⋮ Complex asymptotics of Poincaré functions and properties of Julia sets ⋮ Oscillating heat kernels on ultrametric spaces ⋮ Single-file diffusion on self-similar substrates ⋮ Universal behavior for single-file diffusion on a disordered fractal ⋮ The zeta function of the Laplacian on certain fractals ⋮ VIBRATION SPECTRA OF FINITELY RAMIFIED, SYMMETRIC FRACTALS ⋮ Poincaré Functional Equations, Harmonic Measures on Julia Sets, and Fractal Zeta Functions ⋮ A trace on fractal graphs and the Ihara zeta function ⋮ Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z-graded graphs ⋮ Green functions on self-similar graphs and bounds for the spectrum of the Laplacian

Cites Work

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• Periodic oscillations of coefficients of power series that satisfy functional equations
• Functional iterations and periodic oscillations for simple random walk on the Sierpiński graph
• Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
• Large deviations for Brownian motion on the Sierpiński gasket
• Green functions on self-similar graphs and bounds for the spectrum of the Laplacian
• Pure point spectrum of the Laplacians on fractal graphs
• Transition probabilities for the simple random walk on the Sierpinski graph
• Singularity Analysis of Generating Functions
• Harmonic Calculus on P.C.F. Self-Similar Sets
• Brownian motion on nested fractals
• Markov Chains
• Functional iterations and stopping times for Brownian motion on the Sierpiński gasket
• Spectral properties of self-similar lattices and iteration of rational maps
• The Average Displacement of the Simple Random Walk on the Sierpinski Graph
• Random Walks on Infinite Graphs and Groups
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