Some toy models of self-organized criticality in percolation

zbMath1482.82033arXiv1912.06639MaRDI QIDQ5026480

Raphaël Cerf, Nicolas Forien

Publication date: 8 February 2022

Full work available at URL: https://arxiv.org/abs/1912.06639

zbMATH Keywords

criticalitypercolationself-organized criticality

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27)

Cites Work

• Unnamed Item
• A Curie-Weiss model of self-organized criticality
• Limit theorems for 2D invasion percolation
• Bernoulli and self-destructive percolation on non-amenable graphs
• Seven-dimensional forest fires
• The 2D-Ising model near criticality: a FK-percolation analysis
• Existence of multi-dimensional infinite volume self-organized critical forest-fire models
• Frozen percolation in two dimensions
• The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
• Relations between invasion percolation and critical percolation in two dimensions
• On the invariant distribution of a one-dimensional avalanche process
• Erdős-Renyi random graphs \(+\) forest fires \(=\) self-organized criticality
• Mean field frozen percolation
• The fractal volume of the two-dimensional invasion percolation cluster
• Invasion percolation and the incipient infinite cluster in 2D
• Critical phenomena in natural sciences. Chaos, fractals, selforganization and disorder: concepts and tools.
• Critical exponents for two-dimensional percolation
• The scaling limits of the minimal spanning tree and invasion percolation in the plane
• The scaling limits of near-critical and dynamical percolation
• Sandpile models
• Dynamical evolution of a self-organized-critical percolation model
• On the Wulff crystal in the Ising model.
• Surface order large deviations for Ising, Potts and percolation models
• On the separation profile of infinite graphs
• A planar Ising model of self-organized criticality
• Universality of high-dimensional spanning forests and sandpiles
• The near-critical planar FK-Ising model
• Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models
• The supercritical phase of percolation is well behaved
• Percolation
• The percolation process on a tree where infinite clusters are frozen
• Probability Inequalities for Sums of Bounded Random Variables
• The birth of the infinite cluster: Finite-size scaling in percolation
• Planar lattices do not recover from forest fires