Self-similarity and spectral asymptotics for the continuum random tree

DOI10.1016/j.spa.2007.06.005zbMath1143.60012arXiv1210.6190OpenAlexW1977522959MaRDI QIDQ2483464

Benjamin M. Hambly, David A. Croydon

Publication date: 28 April 2008

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6190

zbMATH Keywords

Heat kernelContinuum random treeSpectral asymptoticsSelf-similar fractal

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Dirichlet forms (31C25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Fractals (28A80) Transition functions, generators and resolvents (60J35)

Related Items (15)

Spectral dimension of simple random walk on a long-range percolation cluster ⋮ Spectral asymptotics of one-dimensional fractal Laplacians in the absence of second-order identities ⋮ Weyl's asymptotic formula for fractal Laplacians defined by a class of self-similar measures with overlaps ⋮ Maximum agreement subtrees and Hölder homeomorphisms between Brownian trees ⋮ Heat Kernel Fluctuations for Stochastic Processes on Fractals and Random Media ⋮ Spectral asymptotics for \(V\)-variable Sierpinski gaskets ⋮ A recursive distributional equation for the stable tree ⋮ Central limit theorems for the spectra of classes of random fractals ⋮ The Hausdorff dimension of a class of random self-similar fractal trees ⋮ Hausdorff measure of arcs and Brownian motion on Brownian spatial trees ⋮ Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice ⋮ Trees and hyperbolicity. The continuum self-similar tree ⋮ Exchangeable hierarchies and mass-structure of weighted real trees ⋮ Brownian motion on stable looptrees ⋮ Self-similar real trees defined as fixed points and their geometric properties

Cites Work

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• On the asymptotics of the eigenvalue counting function for random recursive Sierpinski gaskets
• Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms
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• Harmonic calculus on limits of networks and its application to dendrites
• The continuum random tree. III
• Volume growth and heat kernel estimates for the continuum random tree
• On the convergence of supercritical general (C-M-J) branching processes
• Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture
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