Infinite clusters in dependent automorphism invariant percolation on trees
From MaRDI portal
Publication:1370232
DOI10.1214/aop/1024404518zbMath0895.60098OpenAlexW2090871623MaRDI QIDQ1370232
Publication date: 26 October 1997
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1024404518
Trees (05C05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)
Related Items
Explicit isoperimetric constants and phase transitions in the random-cluster model ⋮ On the speed of random walks on graphs. ⋮ The Ising model on diluted graphs and strong amenability ⋮ Two badly behaved percolation processes on a nonunimodular graph ⋮ A stable marriage of Poisson and Lebesgue ⋮ Minimal spanning forests ⋮ Approximation on slabs and uniqueness for inhomogeneous percolation with a plane of defects ⋮ Neighboring clusters in Bernoulli percolation ⋮ Percolation on nonunimodular transitive graphs ⋮ Friendly Frogs, Stable Marriage, and the Magic of Invariance ⋮ Random nearest neighbor graphs: the translation invariant case ⋮ Harmonic deformation of Delaunay triangulations ⋮ Palm pairs and the general mass-transport principle ⋮ Zero-temperature Glauber dynamics on the 3-regular tree and the median process ⋮ Unimodularity of invariant random subgroups ⋮ Busemann functions and infinite geodesics in two-dimensional first-passage percolation ⋮ Percolation in the hyperbolic plane ⋮ Extremal points of infinite clusters in stationary percolation ⋮ Percolation beyond \(\mathbb Z^{d}\): the contributions of Oded Schramm ⋮ Upper limits of Sinai's walk in random scenery ⋮ The 1-2 model ⋮ Phase transitions on nonamenable graphs ⋮ Invariance, quasi-invariance, and unimodularity for random graphs ⋮ Percolation phenomena in low and high density systems ⋮ Translation-Equivariant Matchings of Coin Flips on ℤd ⋮ Facilitated oriented spin models: some non equilibrium results ⋮ Interacting growth processes and invariant percolation ⋮ Dynamical stability of percolation for some interacting particle systems and \(\varepsilon\)-movability ⋮ Extra heads and invariant allocations ⋮ Critical percolation on any nonamenable group has no infinite clusters ⋮ Invariant 𝜌-percolation on regular trees ⋮ Unimodular Hausdorff and Minkowski dimensions ⋮ Hyperbolic and parabolic unimodular random maps ⋮ Finitely dependent processes are finitary ⋮ Large, lengthy graphs look locally like lines ⋮ The random cluster model on a general graph and a phase transition characterization of nonamenability ⋮ Unimodular measures on the space of all Riemannian manifolds ⋮ Ends of unimodular random manifolds
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Random walks and percolation on trees
- Density and uniqueness in percolation
- Choosing a spanning tree for the integer lattice uniformly
- Random walk in a random environment and first-passage percolation on trees
- Amenability, Kazhdan's property and percolation for trees, groups and equivalence relations
- Topological and metric properties of infinite clusters in stationary two- dimensional site percolation
- Automorphism invariant measures on trees
- Random walks, capacity and percolation on trees
- Tree-indexed random walks on groups and first passage percolation
- Infinite clusters in percolation models
- Percolation and minimal spanning forests in infinite graphs
- The random-cluster model on a homogeneous tree
- Branching processes with local dependencies
- Geometric rate of growth in population-size-dependent branching processes