Volume growth and heat kernel estimates for the continuum random tree

DOI10.1007/s00440-007-0063-4zbMath1133.62066arXivmath/0612585OpenAlexW2059936296MaRDI QIDQ2464674

David A. Croydon

Publication date: 17 December 2007

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

Full work available at URL: https://arxiv.org/abs/math/0612585

zbMATH Keywords

Brownian excursionContinuum random treeHeat kernel estimatesVolume fluctuations

Mathematics Subject Classification ID

Density estimation (62G07) Geometric probability and stochastic geometry (60D05) Markov processes: estimation; hidden Markov models (62M05) Random operators and equations (aspects of stochastic analysis) (60H25) Random measures (60G57) Transition functions, generators and resolvents (60J35)

Related Items (18)

Heat kernel fluctuations for a resistance form with non-uniform volume growth ⋮ Perturbative quantum field theory on random trees ⋮ Heat Kernel Fluctuations for Stochastic Processes on Fractals and Random Media ⋮ Central limit theorems for the spectra of classes of random fractals ⋮ Scaling limit for the random walk on the largest connected component of the critical random graph ⋮ Random walk on the incipient infinite cluster for oriented percolation in high dimensions ⋮ Local limit theorems for sequences of simple random walks on graphs ⋮ Scaling limits for simple random walks on random ordered graph trees ⋮ Self-similarity and spectral asymptotics for the continuum random tree ⋮ 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 ⋮ Heat kernel estimates for FIN processes associated with resistance forms ⋮ Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree ⋮ Stochastic PDEs on graphs as scaling limits of discrete interacting systems ⋮ The gap between Gromov-Vague and Gromov-Hausdorff-vague topology ⋮ Brownian motion on stable looptrees ⋮ Scaling limits of the three-dimensional uniform spanning tree and associated random walk ⋮ Brownian motion on ℝ-trees

Cites Work

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• Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree
• The continuum random tree. I
• Limit of normalized quadrangulations: the Brownian map
• Subdiffusive behavior of random walk on a random cluster
• Excursions in Brownian motion
• Functionals of Brownian meander and Brownian excursion
• Recursive self-similarity for random trees, random triangulations and Brownian excursion
• Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms
• Probabilistic and fractal aspects of Lévy trees
• Brownian motion on the continuum tree
• Harmonic calculus on limits of networks and its application to dendrites
• The continuum random tree. III
• Stability of parabolic Harnack inequalities on metric measure spaces
• Tree-based models for random distribution of mass
• Random walk on the incipient infinite cluster on trees
• The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion
• Packing Measure, and its Evaluation for a Brownian Path
• The exact Hausdorff dimension in random recursive constructions
• Thick and thin points for random recursive fractals
• Heat kernel fluctuations for a resistance form with non-uniform volume growth
• First Passage times and Sojourn Times for Brownian Motion in Space and the Exact Hausdorff Measure of the Sample Path

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