Simple random walk on long range percolation clusters. I: Heat kernel bounds

DOI10.1007/s00440-011-0383-2zbMath1257.82050arXiv0907.2434OpenAlexW1966124616MaRDI QIDQ1934367

Nicholas Crawford, Allan Sly

Publication date: 28 January 2013

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

Full work available at URL: https://arxiv.org/abs/0907.2434

zbMATH Keywords

random walkpercolation process

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Percolation (82B43) Random walks on graphs (05C81)

Related Items (17)

Spectral dimension of simple random walk on a long-range percolation cluster ⋮ Multiple Phase Transitions in Long-Range First-Passage Percolation on Square Lattices ⋮ Recurrence and transience of symmetric random walks with long-range jumps ⋮ Transience and anchored isoperimetric dimension of supercritical percolation clusters ⋮ Scale-free percolation mixing time ⋮ Discrete approximation of symmetric jump processes on metric measure spaces ⋮ Estimates on the effective resistance in anisotropic long-range percolation on \(\mathbb Z^2\) ⋮ Simple random walk on long-range percolation clusters. II: Scaling limits ⋮ The mixing time of a random walk on a long-range percolation cluster in pre-Sierpinski gasket ⋮ Random conductance models with stable-like jumps: quenched invariance principle ⋮ Transience and recurrence of random walks on percolation clusters in an ultrametric space ⋮ Heat kernel estimates for random walks on some kinds of one-dimensional continuum percolation clusters ⋮ Quenched invariance principle for a class of random conductance models with long-range jumps ⋮ Random systems in ultrametric spaces ⋮ Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities ⋮ Random walks on discrete point processes ⋮ The diameter of a long-range percolation cluster on pre-Sierpinski gasket

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