Journal of the European Mathematical Society, ISSN 1435-9855, 2017, Volume 19, Issue 3, pp. 725 - 814

We study bond percolation on the Hamming hypercube {0, 1}(m) around the critical probability p(c...

Mixing time | Non-backtracking random walk | Birth of the giant component | Hypercube | Percolation | Mean-field results | Critical behavior | Scaling window | MATHEMATICS, APPLIED | scaling window | FINITE GRAPHS | critical behavior | N-CUBE | CRITICAL-VALUES | CRITICAL RANDOM GRAPHS | MATHEMATICS | percolation | EVOLUTION | mean-field results | birth of the giant component | non-backtracking random walk | BOOTSTRAP PERCOLATION | PHASE-TRANSITION | EXPANSION | COMPONENT | RANDOM SUBGRAPHS | mixing time

Mixing time | Non-backtracking random walk | Birth of the giant component | Hypercube | Percolation | Mean-field results | Critical behavior | Scaling window | MATHEMATICS, APPLIED | scaling window | FINITE GRAPHS | critical behavior | N-CUBE | CRITICAL-VALUES | CRITICAL RANDOM GRAPHS | MATHEMATICS | percolation | EVOLUTION | mean-field results | birth of the giant component | non-backtracking random walk | BOOTSTRAP PERCOLATION | PHASE-TRANSITION | EXPANSION | COMPONENT | RANDOM SUBGRAPHS | mixing time

Journal Article

Physics reports, ISSN 0370-1573, 2015, Volume 578, pp. 1 - 32

Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component...

Earth topography | Percolation | Ising model | Explosive percolation | SLE | DENSITY SERIES EXPANSIONS | OPTIMAL CHANNEL NETWORKS | PHYSICS, MULTIDISCIPLINARY | RANDOM GAUSSIAN SURFACES | MOLECULAR-SIZE DISTRIBUTION | RANDOM-CLUSTER MODEL | FOREST-FIRE MODEL | RANGE CORRELATED PERCOLATION | BOOTSTRAP PERCOLATION | URBAN-GROWTH PATTERNS | 3D ISING-MODEL | Physics - Statistical Mechanics

Earth topography | Percolation | Ising model | Explosive percolation | SLE | DENSITY SERIES EXPANSIONS | OPTIMAL CHANNEL NETWORKS | PHYSICS, MULTIDISCIPLINARY | RANDOM GAUSSIAN SURFACES | MOLECULAR-SIZE DISTRIBUTION | RANDOM-CLUSTER MODEL | FOREST-FIRE MODEL | RANGE CORRELATED PERCOLATION | BOOTSTRAP PERCOLATION | URBAN-GROWTH PATTERNS | 3D ISING-MODEL | Physics - Statistical Mechanics

Journal Article

Journal of graph theory, ISSN 1097-0118, 2019, Volume 94, Issue 2, pp. 252 - 266

Bootstrap percolation is a deterministic cellular automaton in which vertices of a graph G begin in one of two states, “dormant” or “active...

ore condition | bootstrap percolation | chvàtal condition | MATHEMATICS | chvatal condition | CONTAGIOUS SETS

ore condition | bootstrap percolation | chvàtal condition | MATHEMATICS | chvatal condition | CONTAGIOUS SETS

Journal Article

Physical Review Letters, ISSN 0031-9007, 10/2011, Volume 107, Issue 17, p. 175703

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage...

EXPLOSIVE PERCOLATION | PHYSICS, MULTIDISCIPLINARY | COMPLEX NETWORKS | LATTICE | BOOTSTRAP PERCOLATION

EXPLOSIVE PERCOLATION | PHYSICS, MULTIDISCIPLINARY | COMPLEX NETWORKS | LATTICE | BOOTSTRAP PERCOLATION

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2012, Volume 364, Issue 5, pp. 2667 - 2701

In r-neighbour bootstrap percolation on a graph G, a (typically random) set A of initially 'infected' vertices spreads by infecting (at each time step...

Mathematical sets | Cardinality | Rectangles | Ising model | Mathematics | Grants | Cellular automata | Vertices | Induction assumption | Metastability | MATHEMATICS | TREES | MODELS | Bootstrap percolation | BEHAVIOR | GROWTH | sharp threshold | METASTABILITY THRESHOLD

Mathematical sets | Cardinality | Rectangles | Ising model | Mathematics | Grants | Cellular automata | Vertices | Induction assumption | Metastability | MATHEMATICS | TREES | MODELS | Bootstrap percolation | BEHAVIOR | GROWTH | sharp threshold | METASTABILITY THRESHOLD

Journal Article

Probability theory and related fields, ISSN 0178-8051, 10/2018, Volume 172, Issue 1-2, pp. 191 - 243

We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with (1, 2...

DIMENSIONS | Finite-size effects | CELLULAR-AUTOMATA | MODELS | Bootstrap percolation | SHARP METASTABILITY THRESHOLD | Sharp threshold | To be checked by Faculty | Metastability | 82C43 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | 82B43 | Quantitative Finance | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | 60K35 | STATISTICS & PROBABILITY | Metastable phases | Anisotropy | Asymptotic properties | Lattices | Two dimensional models | Percolation | Phase transitions

DIMENSIONS | Finite-size effects | CELLULAR-AUTOMATA | MODELS | Bootstrap percolation | SHARP METASTABILITY THRESHOLD | Sharp threshold | To be checked by Faculty | Metastability | 82C43 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | 82B43 | Quantitative Finance | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | 60K35 | STATISTICS & PROBABILITY | Metastable phases | Anisotropy | Asymptotic properties | Lattices | Two dimensional models | Percolation | Phase transitions

Journal Article

The Annals of probability, ISSN 0091-1798, 7/2009, Volume 37, Issue 4, pp. 1329 - 1380

By bootstrap percolation we mean the following deterministic process on a graph G...

Probability distributions | Rectangles | Plant roots | Cubes | Mathematical inequalities | Grants | Cellular automata | Vertices | Induction assumption | Metastability | Bootstrap percolation | Sharp threshold | GRAPH | INEQUALITIES | MODELS | BEHAVIOR | PROOF | STATISTICS & PROBABILITY | HYPERCUBE | sharp threshold | METASTABILITY THRESHOLD | 60C05 | 60K35

Probability distributions | Rectangles | Plant roots | Cubes | Mathematical inequalities | Grants | Cellular automata | Vertices | Induction assumption | Metastability | Bootstrap percolation | Sharp threshold | GRAPH | INEQUALITIES | MODELS | BEHAVIOR | PROOF | STATISTICS & PROBABILITY | HYPERCUBE | sharp threshold | METASTABILITY THRESHOLD | 60C05 | 60K35

Journal Article

8.
Full Text
ERRATUM TO "SHARP METASTABILITY THRESHOLD FOR AN ANISOTROPIC BOOTSTRAP PERCOLATION MODEL"

The Annals of probability, ISSN 0091-1798, 3/2016, Volume 44, Issue 2, pp. 1599 - 1599

We provide an Erratum, correcting how our main result generalises and correct some steps in the proof.

metastability | sharp threshold | Bootstrap percolation | anisotropy | Sharp threshold | Anisotropy | Metastability | 83C43 | 83B43 | 60K35

metastability | sharp threshold | Bootstrap percolation | anisotropy | Sharp threshold | Anisotropy | Metastability | 83C43 | 83B43 | 60K35

Journal Article

The Annals of applied probability, ISSN 1050-5164, 10/2012, Volume 22, Issue 5, pp. 1989 - 2047

Bootstrap percolation on the random graph G n,p is a process of spread of "activation" on a given realization of the graph with a given number of initially active nodes...

Epidemics | Determinism | Roots of functions | Approximation | Disease models | Infections | Random variables | Martingales | Vertices | Dynamic modeling | Bootstrap percolation | Sharp threshold | Random graph | FINAL-SIZE | THRESHOLD | random graph | EPIDEMIC MODEL | STATISTICS & PROBABILITY | NETWORKS | sharp threshold | Naturvetenskap | Mathematics | Natural Sciences | Matematik | Sannolikhetsteori och statistik | Probability Theory and Statistics

Epidemics | Determinism | Roots of functions | Approximation | Disease models | Infections | Random variables | Martingales | Vertices | Dynamic modeling | Bootstrap percolation | Sharp threshold | Random graph | FINAL-SIZE | THRESHOLD | random graph | EPIDEMIC MODEL | STATISTICS & PROBABILITY | NETWORKS | sharp threshold | Naturvetenskap | Mathematics | Natural Sciences | Matematik | Sannolikhetsteori och statistik | Probability Theory and Statistics

Journal Article

Random Structures & Algorithms, ISSN 1042-9832, 12/2018, Volume 53, Issue 4, pp. 638 - 651

We study the following bootstrap percolation process: given a connected graph G, a constant ρ ∈ [0,1...

bootstrap percolation | contagious sets | irreversible dynamic monopolies | MATHEMATICS, APPLIED | SIZE | TRIGGERING CASCADES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | DIMENSIONS | THRESHOLD | DYNAMIC MONOPOLIES | BOUNDS | CONNECTED GRAPHS | HYPERCUBE | Percolation | Graph theory

bootstrap percolation | contagious sets | irreversible dynamic monopolies | MATHEMATICS, APPLIED | SIZE | TRIGGERING CASCADES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | DIMENSIONS | THRESHOLD | DYNAMIC MONOPOLIES | BOUNDS | CONNECTED GRAPHS | HYPERCUBE | Percolation | Graph theory

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 10/2019, Volume 175, Issue 1, pp. 467 - 486

In the polluted bootstrap percolation model, the vertices of a graph are independently declared initially occupied with probability p or closed with probability q...

Statistics for Business, Management, Economics, Finance, Insurance | Cellular automaton | Critical scaling | Mathematical and Computational Biology | Bootstrap percolation | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | 82B43 | 60K35 | Quantitative Finance | DYNAMICS | STATISTICS & PROBABILITY | SHARP METASTABILITY THRESHOLD | Percolation | Graph theory | Cubic lattice | Apexes

Statistics for Business, Management, Economics, Finance, Insurance | Cellular automaton | Critical scaling | Mathematical and Computational Biology | Bootstrap percolation | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | 82B43 | 60K35 | Quantitative Finance | DYNAMICS | STATISTICS & PROBABILITY | SHARP METASTABILITY THRESHOLD | Percolation | Graph theory | Cubic lattice | Apexes

Journal Article

Scientific Reports, ISSN 2045-2322, 07/2015, Volume 5, Issue 1, p. 11905

Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena...

MULTIDISCIPLINARY SCIENCES | EXPLOSIVE PERCOLATION | BOOTSTRAP PERCOLATION | Phase transitions | Size distribution | Physics - Statistical Mechanics

MULTIDISCIPLINARY SCIENCES | EXPLOSIVE PERCOLATION | BOOTSTRAP PERCOLATION | Phase transitions | Size distribution | Physics - Statistical Mechanics

Journal Article

The Annals of applied probability, ISSN 1050-5164, 2/2015, Volume 25, Issue 1, pp. 287 - 323

.... Bootstrap percolation with threshold θ starts with a random set of open vertices, to which every vertex belongs independently with probability p, and at each time step the open set grows by adjoining every vertex with at least θ open neighbors...

Poisson convergence | Critical exponent | Hamming torus | Bootstrap percolation | GRAPH | DIMENSIONS | CELLULAR-AUTOMATA | critical exponent | STATISTICS & PROBABILITY | SHARP THRESHOLD | HYPERCUBE | RANDOM SUBGRAPHS | Mathematics - Probability | 60K35

Poisson convergence | Critical exponent | Hamming torus | Bootstrap percolation | GRAPH | DIMENSIONS | CELLULAR-AUTOMATA | critical exponent | STATISTICS & PROBABILITY | SHARP THRESHOLD | HYPERCUBE | RANDOM SUBGRAPHS | Mathematics - Probability | 60K35

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 01/2016, Volume 126, Issue 1, pp. 234 - 264

On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process...

Random geometric graph | Hyperbolic plane | Percolation | Bootstrap percolation | STATISTICS & PROBABILITY | EMERGENCE

Random geometric graph | Hyperbolic plane | Percolation | Bootstrap percolation | STATISTICS & PROBABILITY | EMERGENCE

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 08/2008, Volume 78, Issue 2, p. 022101

The k-core percolation on the Bethe lattice has been proposed as a simple model of the jamming transition because of its hybrid first-order-second-order nature, We investigate numerically k-core...

BICONNECTEDNESS | UNIVERSALITY | CELLULAR-AUTOMATA | THRESHOLD | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | SYSTEMS | BETHE LATTICE | PHYSICS, MATHEMATICAL | 2-DIMENSIONAL BOOTSTRAP PERCOLATION | Physics - Disordered Systems and Neural Networks

BICONNECTEDNESS | UNIVERSALITY | CELLULAR-AUTOMATA | THRESHOLD | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | SYSTEMS | BETHE LATTICE | PHYSICS, MATHEMATICAL | 2-DIMENSIONAL BOOTSTRAP PERCOLATION | Physics - Disordered Systems and Neural Networks

Journal Article

The Annals of probability, ISSN 0091-1798, 7/2015, Volume 43, Issue 4, pp. 1731 - 1776

We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of...

Additivity | Percolation | Cellular automaton | Quasireplicator | Ether | Replicator | DEPENDENT PERCOLATION | ether | SNOWFLAKES | STATISTICS & PROBABILITY | quasireplicator | SEEDS | DIMENSIONS | THRESHOLD | percolation | REPLICATION | BOOTSTRAP PERCOLATION | replicator | cellular automaton | 37B15 | 60K35

Additivity | Percolation | Cellular automaton | Quasireplicator | Ether | Replicator | DEPENDENT PERCOLATION | ether | SNOWFLAKES | STATISTICS & PROBABILITY | quasireplicator | SEEDS | DIMENSIONS | THRESHOLD | percolation | REPLICATION | BOOTSTRAP PERCOLATION | replicator | cellular automaton | 37B15 | 60K35

Journal Article

ACM Transactions on Knowledge Discovery from Data (TKDD), ISSN 1556-4681, 03/2018, Volume 12, Issue 2, pp. 1 - 39

.... Indeed, by exploiting a sufficiently large set of seed nodes, a percolation process can correctly match almost all nodes across the different social networks...

bootstrap percolation | de-anonymization | Graph matching | Bootstrap percolation | De-anonymization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INFORMATION SYSTEMS | ALGORITHM

bootstrap percolation | de-anonymization | Graph matching | Bootstrap percolation | De-anonymization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INFORMATION SYSTEMS | ALGORITHM

Journal Article

Random Structures & Algorithms, ISSN 1042-9832, 07/2018, Volume 52, Issue 4, pp. 597 - 616

We study a new geometric bootstrap percolation model, line percolation, on the d...

bootstrap percolation | critical probability | polynomial method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | DIMENSIONS | MATHEMATICS, APPLIED | INEQUALITIES | MODELS | SHARP METASTABILITY THRESHOLD | Analysis | Disease transmission | Set theory | Percolation | Infections | Parameters

bootstrap percolation | critical probability | polynomial method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | DIMENSIONS | MATHEMATICS, APPLIED | INEQUALITIES | MODELS | SHARP METASTABILITY THRESHOLD | Analysis | Disease transmission | Set theory | Percolation | Infections | Parameters

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 08/2012, Volume 86, Issue 6

Quantum k-core percolation is the study of quantum transport on k-core percolation clusters where each occupied bond must have at least k occupied neighboring bonds...

UNIVERSALITY | PHYSICS, CONDENSED MATTER | METAL-INSULATOR-TRANSITION | PHYSICS, APPLIED | SUDDEN EMERGENCE | BOOTSTRAP | MATERIALS SCIENCE, MULTIDISCIPLINARY | DIFFUSION | MODEL | Physics - Disordered Systems and Neural Networks

UNIVERSALITY | PHYSICS, CONDENSED MATTER | METAL-INSULATOR-TRANSITION | PHYSICS, APPLIED | SUDDEN EMERGENCE | BOOTSTRAP | MATERIALS SCIENCE, MULTIDISCIPLINARY | DIFFUSION | MODEL | Physics - Disordered Systems and Neural Networks

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 10/2016, Volume 166, Issue 1, pp. 321 - 364

We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on $$[n]^2$$ [ n...

Concentration of measure | Primary 60K35 | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Bootstrap percolation | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Operation Research/Decision Theory | Quantitative Finance | Secondary 60C05 | STATISTICS & PROBABILITY | SHARP METASTABILITY THRESHOLD | Studies | Probability | Bootstrap method | Mathematical analysis | Texts | Percolation | Constants | Probability theory

Concentration of measure | Primary 60K35 | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Bootstrap percolation | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Operation Research/Decision Theory | Quantitative Finance | Secondary 60C05 | STATISTICS & PROBABILITY | SHARP METASTABILITY THRESHOLD | Studies | Probability | Bootstrap method | Mathematical analysis | Texts | Percolation | Constants | Probability theory

Journal Article