Recent advances and open challenges in percolation

Abstract

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation.

References in corpus (86)

• Emergence of scaling in random networks
• Catastrophic cascade of failures in interdependent networks
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• k-core organization of complex networks
• Explosive Synchronization Transitions in Scale-free Networks
• Universal behavior in a generalized model of contagion
• A fast Monte Carlo algorithm for site or bond percolation
• Efficient Monte Carlo algorithm and high-precision results for percolation
• Are randomly grown graphs really random?
• Method for Generating Long-Range Correlations for Large Systems
• Critical Percolation in Finite Geometries
• "Explosive Percolation" Transition is Actually Continuous
• Modeling Urban Growth Patterns with Correlated Percolation
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Dynamics of jamming transitions in complex networks
• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Exact solution of site and bond percolation on small-world networks
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
• Explosive percolation via control of the largest cluster
• Percolation Transitions in Scale-Free Networks under Achlioptas Process
• Conformally Invariant Fractals and Potential Theory
• Conductivity Exponent and Backbone Dimension in 2-d Percolation
• Construction and Analysis of Random Networks with Explosive Percolation
• Local cluster aggregation models of explosive percolation
• Avoiding a Spanning Cluster in Percolation Models
• A Generalized Epidemic Process and Tricritical Dynamic Percolation
• A crossing probability for critical percolation in two dimensions
• The boundary between long-range and short-range critical behavior
• Strongly discontinuous explosive percolation with multiple giant components
• Scaling behavior of explosive percolation on the square lattice
• Ordinary Percolation with Discontinuous Transitions
• Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
• Cluster aggregation model for discontinuous percolation transition
• Nonlinear Measures for Characterizing Rough Surface Morphologies
• Universal amplitude ratios in the two-dimensional $q$-state Potts model and percolation from quantum field theory
• Outbreaks of coinfections: the critical role of cooperativity
• Universality of finite-size corrections to the number of critical percolation clusters
• Influence of long-range interactions on the critical behavior of the Ising model
• Exact bond percolation thresholds in two dimensions
• Percolation with long-range correlated disorder
• Watersheds are Schramm-Loewner Evolution curves
• Shape-dependent universality in percolation
• Fracturing ranked surfaces
• The Harris-Luck criterion for random lattices
• Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
• Site-diluted three dimensional Ising Model with long-range correlated disorder
• Two-dimensional SIR epidemics with long range infection
• Depinning of a domain wall in the 2d random-field Ising model
• Percolation Crossing Formulas and Conformal Field Theory
• Percolation description of the global topography of Earth and Moon
• Deriving an underlying mechanism for discontinuous percolation
• Optimal path cracks in correlated and uncorrelated lattices
• New efficient methods to calculate watersheds
• Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations
• Impact of Perturbations on Watersheds
• Pair Connectedness and Shortest Path Scaling in Critical Percolation
• SIR epidemics with long range infection in one dimension
• Transfer matrix computation of critical polynomials for two-dimensional Potts models
• Finite-size scaling of the stochastic susceptible-infected-recovered model
• Retention capacity of random surfaces
• Long-range epidemic spreading with immunization
• Exact critical exponent for the shortest-path scaling function in percolation
• The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices
• Correlated quantum percolation in the lowest Landau level
• Critical behavior of the Random-Field Ising Magnet with long range correlated disorder
• Percolation in the canonical ensemble
• Statistics of the critical percolation backbone with spatial long-range correlations
• Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines
• Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets
• Stacked triangular lattice: Percolation properties
• High-precision Estimate of the Critical Exponents for the Directed Ising Universality Class
• A percolation model with continuously varying exponents
• Random Sequential Renormalization of Networks I: Application to Critical Trees
• Irreversible Aggregation and Network Renormalization
• Agglomerative Percolation on Bipartite Networks: A Novel Type of Spontaneous Symmetry Breaking
• How to share underground reservoirs
• Random Sequential Renormalization and Agglomerative Percolation in Networks: Application to Erd"os-R'enyi and Scale-free Graphs
• Monte-Carlo study of scaling exponents of rough surfaces and correlated percolation
• Critical condition of the water-retention model
• Critical exponents of the pair contact process with diffusion
• Exact evaluation of the cutting path length in a percolation model on a hierarchical network
• Analysis on the evolution process of BFW-like model with explosive percolation of multiple giant components
• An exact universal amplitude ratio for percolation

Cited by in corpus (81)

• Robustness and resilience of complex networks
• Recent advances in percolation theory and its applications
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Percolation on complex networks: Theory and application
• Explosive Phenomena in Complex Networks
• Explosive Percolation: Novel critical and supercritical phenomena
• Cascading Failures in Complex Networks
• Higher-order percolation processes on multiplex hypergraphs
• Recent advances of percolation theory in complex networks
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• The dynamic nature of percolation on networks with triadic interactions
• Rare events and discontinuous percolation transitions
• Topological Percolation on Hyperbolic Simplicial Complexes
• One-dimensional long-range percolation: a numerical study
• Clique percolation in random graphs
• You Can Run, You Can Hide: The Epidemiology and Statistical Mechanics of Zombies
• Large deviation theory of percolation on multiplex networks
• Universal mechanism for hybrid percolation transitions
• First-order phase transitions in outbreaks of co-infectious diseases and the extended general epidemic process
• Homological percolation transitions in growing simplicial complexes
• Diverse types of percolation transitions
• Tackling the subsampling problem to infer collective properties from limited data
• Percolation on branching simplicial and cell complexes and its relation to interdependent percolation
• Critical percolation clusters in seven dimensions and on a complete graph
• Critical fragmentation properties of random drilling: How many random holes need to be drilled to collapse a wooden cube?
• Universal Finite-Size Scaling for Percolation Theory in High Dimensions
• A universal approach for drainage basins
• Phase Transitions and Criticality in the Collective Behavior of Animals -- Self-organization and biological function
• Renormalization group for link percolation on planar hyperbolic manifolds
• Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
• Jamming and percolation properties of random sequential adsorption with relaxation
• Universality and Asymptotic Scaling in Drilling Percolation
• Percolation in a distorted square lattice
• Critical behavior of a two-step contagion model with multiple seeds
• Universality classes of generalized epidemic process on random networks
• Renormalization group theory for percolation in time-varying networks
• Two-dimensional systems of elongated particles: From diluted to dense
• Percolation model with an additional source of disorder
• $N$-cluster correlations in four- and five-dimensional percolation
• Inverting the Achlioptas rule for explosive percolation
• From explosive to infinite-order transitions on a hyperbolic network
• Critical phenomena of a hybrid phase transition in cluster merging dynamics
• Unified framework for hybrid percolation transitions based on microscopic dynamics
• Emergence of coexisting percolating clusters in networks
• Tricritical directed percolation with long-range interaction in one and two dimensions
• Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems
• Information entropy of classical versus explosive percolation
• Colored Percolation
• Effect of chemical short-range order and percolation on passivation in binary alloys
• Percolation and jamming of linear $k$-mers on square lattice with defects: effect of anisotropy
• Depinning in the quenched Kardar-Parisi-Zhang class I: Mappings, simulations and algorithm
• Percolation on Hypergraphs with Four-Edges
• History-dependent percolation in two dimensions
• Homophily Within and Across Groups
• Role of hubs in the synergistic spread of behavior
• Level Set Percolation in Two-Dimensional Gaussian Free Field
• Percolation of the Site Random-Cluster Model by Monte Carlo Method
• Exploring Percolative Landscapes: Infinite Cascades of Geometric Phase Transitions
• Critical clusters in liquid crystals: Fractal geometry and conformal invariance
• Coastlines violate the Schramm-Loewner Evolution
• A hybrid percolation transition at a finite transition point in scale-free networks
• Clusters' size-degree distribution for bond percolation
• Percolation Transitions in Growing Networks Under Achlioptas Processes: Analytic Solutions
• $K$-selective percolation: A simple model leading to a rich repertoire of phase transitions
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states
• Maximal Density, Kinetics of Deposition and Percolation Threshold of Loose Packed Lattices
• Chase-Escape Percolation on the 2D Square Lattice
• Dynamical Crossover in Invasion Percolation
• Double Transition in a Model of Oscillating Percolation
• Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition
• Percolation study for the capillary ascent of a liquid through a granular soil
• Janus Percolation in Anisotropic Limited-Degree Networks
• Direct Observation of Quantum Percolation Dynamics
• Exact Results for Average Cluster Numbers in Bond Percolation on Infinite-Length Lattice Strips
• How universal is the mean-field universality class for percolation in complex networks?
• Anomalous criticality coexists with giant cluster in the uniform forest model
• Discontinuous emergence of a giant cluster in assortative scale-free networks
• Variation of the critical percolation threshold in the Achlioptas processes
• Universal fluctuations and ergodicity of generalized diffusivity on critical percolation clusters
• Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks