Probability Surveys, ISSN 1549-5787, 2018, Volume 15, pp. 243 - 306

Journal Article

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, ISSN 0027-8424, 02/2019, Volume 116, Issue 8, pp. 2821 - 2830

The abelian sandpile is a cellular automaton which serves as the archetypical model to study self-organized criticality, a phenomenon occurring in various...

criticality | abelian sandpile | dynamics | identity | MULTIDISCIPLINARY SCIENCES | Computer Simulation | Models, Statistical | Transformation | Fractals | Cellular automata | Biological activity | Harmonic functions | Domains | Dynamics | Markov processes | Evolution | Scaling | Stochasticity | Configurations | Translations | Self-similarity | Physical Sciences | PNAS Plus

criticality | abelian sandpile | dynamics | identity | MULTIDISCIPLINARY SCIENCES | Computer Simulation | Models, Statistical | Transformation | Fractals | Cellular automata | Biological activity | Harmonic functions | Domains | Dynamics | Markov processes | Evolution | Scaling | Stochasticity | Configurations | Translations | Self-similarity | Physical Sciences | PNAS Plus

Journal Article

Journal d'Analyse Mathématique, ISSN 0021-7670, 7/2019, Volume 138, Issue 1, pp. 361 - 403

We introduce a new lattice growth model, which we call the boundary sandpile. The model amounts to potential-theoretic redistribution of a given initial mass...

Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | EXISTENCE | MATHEMATICS | FLUCTUATIONS | AGGREGATION | INTERNAL DLA | Odometers | Regularity | Free boundaries | free boundary | Matematisk analys | quadrature surface | asymptotic shape | lattice growth model | Boundary sandpile | Mathematical Analysis | balayage | Naturvetenskap | Abelian sandpile | Natural Sciences | Matematik | divisible sandpile

Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | EXISTENCE | MATHEMATICS | FLUCTUATIONS | AGGREGATION | INTERNAL DLA | Odometers | Regularity | Free boundaries | free boundary | Matematisk analys | quadrature surface | asymptotic shape | lattice growth model | Boundary sandpile | Mathematical Analysis | balayage | Naturvetenskap | Abelian sandpile | Natural Sciences | Matematik | divisible sandpile

Journal Article

JOURNAL OF STATISTICAL PHYSICS, ISSN 0022-4715, 02/2020, Volume 178, Issue 3, pp. 711 - 724

We introduce a natural stochastic extension, called SSP, of the abelian sandpile model (ASM), which shares many mathematical properties with ASM, yet radically...

STATE | Abelian sandpile model | The LLL algorithm | PHYSICS, MATHEMATICAL | Stochastic sandpile model | Lattice reduction

STATE | Abelian sandpile model | The LLL algorithm | PHYSICS, MATHEMATICAL | Stochastic sandpile model | Lattice reduction

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 12/2018, Volume 511, pp. 358 - 370

A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with shortcut density ϕ, ϕ=0 represents a regular...

Sandpile model | Self-organized criticality | Small-world networks | TRANSITION | UNIVERSALITY | EVENTS | PHYSICS, MULTIDISCIPLINARY | FIELD | DYNAMICS | ABELIAN SANDPILE

Sandpile model | Self-organized criticality | Small-world networks | TRANSITION | UNIVERSALITY | EVENTS | PHYSICS, MULTIDISCIPLINARY | FIELD | DYNAMICS | ABELIAN SANDPILE

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2018, Volume 51, Issue 1, p. 15002

We consider the Abelian sandpile model on triangular and hexagonal lattices. We compute several height probabilities on the full plane and on half-planes, and...

logarithmic conformal field theory | uniform spanning trees | Abelian sandpile model | 2-DIMENSIONAL ABELIAN SANDPILE | PHYSICS, MULTIDISCIPLINARY | SPANNING-TREES | MODEL | PHYSICS, MATHEMATICAL | CRITICAL EXPONENTS | GRAPHS | HEIGHT CORRELATIONS | WAVES | CONFORMAL FIELD-THEORY | VARIABLES | AVALANCHES

logarithmic conformal field theory | uniform spanning trees | Abelian sandpile model | 2-DIMENSIONAL ABELIAN SANDPILE | PHYSICS, MULTIDISCIPLINARY | SPANNING-TREES | MODEL | PHYSICS, MATHEMATICAL | CRITICAL EXPONENTS | GRAPHS | HEIGHT CORRELATIONS | WAVES | CONFORMAL FIELD-THEORY | VARIABLES | AVALANCHES

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 02/2018, Volume 154, pp. 145 - 171

We prove several results concerning a polynomial that arises from the sandpile model on directed graphs; these results are previously only known for undirected...

Greedoid | Tutte polynomial | Abelian sandpile model | Chip firing game | G-parking function | MATHEMATICS | CHIP-FIRING GAMES | SPANNING-TREES | POTENTIAL-THEORY | G-PARKING FUNCTIONS | Mathematics - Combinatorics

Greedoid | Tutte polynomial | Abelian sandpile model | Chip firing game | G-parking function | MATHEMATICS | CHIP-FIRING GAMES | SPANNING-TREES | POTENTIAL-THEORY | G-PARKING FUNCTIONS | Mathematics - Combinatorics

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2019, Volume 372, Issue 12, pp. 8307 - 8345

The abelian sandpile model defines a Markov chain whose states are integer-valued functions on the vertices of a simple connected graph G. By viewing this...

sandpile group | Abelian sandpile model | CHIP-FIRING GAMES | SPANNING-TREES | pseudoinverse | STATE | smoothing parameter | Laplacian lattice | MATHEMATICS | chip-firing | multiplicative harmonic function | spectral gap | EXPANDER GRAPHS | LATTICE | mixing time

sandpile group | Abelian sandpile model | CHIP-FIRING GAMES | SPANNING-TREES | pseudoinverse | STATE | smoothing parameter | Laplacian lattice | MATHEMATICS | chip-firing | multiplicative harmonic function | spectral gap | EXPANDER GRAPHS | LATTICE | mixing time

Journal Article

Comptes rendus - Mathématique, ISSN 1631-073X, 02/2016, Volume 354, Issue 2, pp. 125 - 130

We study a sandpile model on the set of the lattice points in a large lattice polygon. A small perturbation ψ of the maximal stable state μ≡3 is obtained by...

Combinatorics | Mathematical physics | MATHEMATICS | MODEL | ABELIAN SANDPILE

Combinatorics | Mathematical physics | MATHEMATICS | MODEL | ABELIAN SANDPILE

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 3/2014, Volume 27, Issue 1, pp. 153 - 167

We give a new simple construction of the sandpile measure on an infinite graph G, under the sole assumption that each tree in the Wired Uniform Spanning Forest...

Minimal configuration | Abelian sandpile | Determinantal process | Probability Theory and Stochastic Processes | Sandpile measure | Mathematics | Statistics, general | Uniform spanning tree | 82C20 | 60K35 | SELF-ORGANIZED CRITICALITY | STATISTICS & PROBABILITY | INFINITE VOLUME LIMIT | MODEL | UNIFORM SPANNING FORESTS | GRAPHS | Mathematics - Probability

Minimal configuration | Abelian sandpile | Determinantal process | Probability Theory and Stochastic Processes | Sandpile measure | Mathematics | Statistics, general | Uniform spanning tree | 82C20 | 60K35 | SELF-ORGANIZED CRITICALITY | STATISTICS & PROBABILITY | INFINITE VOLUME LIMIT | MODEL | UNIFORM SPANNING FORESTS | GRAPHS | Mathematics - Probability

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 04/2007, Volume 75, Issue 4, p. 041122

Rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in...

SELF-ORGANIZED CRITICALITY | PHYSICS, FLUIDS & PLASMAS | ABSORBING STATES | DYNAMICS | UNIVERSALITY CLASSES | AVOIDING WALKS | CRITICAL-BEHAVIOR | ABELIAN SANDPILE | PHYSICS, MATHEMATICAL | TANG-WIESENFELD SANDPILE | AVALANCHES | CRITICAL EXPONENTS | Physics - Soft Condensed Matter

SELF-ORGANIZED CRITICALITY | PHYSICS, FLUIDS & PLASMAS | ABSORBING STATES | DYNAMICS | UNIVERSALITY CLASSES | AVOIDING WALKS | CRITICAL-BEHAVIOR | ABELIAN SANDPILE | PHYSICS, MATHEMATICAL | TANG-WIESENFELD SANDPILE | AVALANCHES | CRITICAL EXPONENTS | Physics - Soft Condensed Matter

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 2019, Volume 177, Issue 1-2, pp. 369 - 396

We show that in Abelian sandpiles on infinite Galton–Watson trees, the probability that the total avalanche has more than t topplings decays as t- 1 / 2. We...

Uniform spanning tree | Conductance martingale | Abelian sandpile | Wired spanning forest | STATISTICS & PROBABILITY | INFINITE VOLUME LIMIT | MODEL | Trees | Resistance | Trees (mathematics) | Avalanches | Martingales | Probability | Mathematics

Uniform spanning tree | Conductance martingale | Abelian sandpile | Wired spanning forest | STATISTICS & PROBABILITY | INFINITE VOLUME LIMIT | MODEL | Trees | Resistance | Trees (mathematics) | Avalanches | Martingales | Probability | Mathematics

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 07/2018, Volume 25, Issue 3

An EW-tableau is a certain 0/1-filling of a Ferrers diagram, corresponding uniquely to an acyclic orientation, with a unique sink, of a certain bipartite graph...

NEW-tableaux | Abelian sandpile model | EW-tableaux | Permutation tableaux | Permutation statistics | tree-like tableaux | Le-tableaux | MATHEMATICS | MATHEMATICS, APPLIED | COMPLETE BIPARTITE GRAPH | PERMUTATION TABLEAUX

NEW-tableaux | Abelian sandpile model | EW-tableaux | Permutation tableaux | Permutation statistics | tree-like tableaux | Le-tableaux | MATHEMATICS | MATHEMATICS, APPLIED | COMPLETE BIPARTITE GRAPH | PERMUTATION TABLEAUX

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 01/2010, Volume 138, Issue 1, pp. 143 - 159

htmlabstractWe study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Z^d. Any site with at...

growth model | dimensional reduction | abelian sandpile | least action principle | bootstrap percolation | discrete Laplacian | Dimensional reduction | Growth model | Discrete Laplacian | Least action principle | Bootstrap percolation | Abelian sandpile | PHYSICS, MATHEMATICAL | Analysis | Explosions

growth model | dimensional reduction | abelian sandpile | least action principle | bootstrap percolation | discrete Laplacian | Dimensional reduction | Growth model | Discrete Laplacian | Least action principle | Bootstrap percolation | Abelian sandpile | PHYSICS, MATHEMATICAL | Analysis | Explosions

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 5/2008, Volume 141, Issue 1, pp. 181 - 212

We study the Abelian sandpile model on $${\mathbb{Z}}^{d}$$ . In d ≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect...

Loop-erased random walk | Abelian sandpile model | 82C22 | Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Tail triviality | Quantitative Finance | Wave | Two-component spanning tree | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Mathematical Biology in General | Uniform spanning tree | 60K35 | Addition operator | loop-erased random walk | two-component spanning tree | SELF-ORGANIZED CRITICALITY | addition operator | tail triviality | uniform spanning tree | TREE | STATISTICS & PROBABILITY | wave | Studies | Probability | Random walk theory | Markov analysis

Loop-erased random walk | Abelian sandpile model | 82C22 | Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Tail triviality | Quantitative Finance | Wave | Two-component spanning tree | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Mathematical Biology in General | Uniform spanning tree | 60K35 | Addition operator | loop-erased random walk | two-component spanning tree | SELF-ORGANIZED CRITICALITY | addition operator | tail triviality | uniform spanning tree | TREE | STATISTICS & PROBABILITY | wave | Studies | Probability | Random walk theory | Markov analysis

Journal Article

Geometric and Functional Analysis, ISSN 1016-443X, 2/2016, Volume 26, Issue 1, pp. 306 - 336

The Abelian sandpile process evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing one of its chips...

Analysis | Abelian sandpile | Scaling limit | Viscosity solution | Apollonian triangulation | Apollonian circle packing | Mathematics | 35R35 | 60K35 | Obstacle problem | MATHEMATICS | VISCOSITY SOLUTIONS

Analysis | Abelian sandpile | Scaling limit | Viscosity solution | Apollonian triangulation | Apollonian circle packing | Mathematics | 35R35 | 60K35 | Obstacle problem | MATHEMATICS | VISCOSITY SOLUTIONS

Journal Article

Electronic Journal of Probability, ISSN 1083-6489, 2017, Volume 22

Consider the Abelian sandpile measure on Z(d), d >= 2, obtained as the L -> infinity limit of the stationary distribution of the sandpile on [-L, L](d) boolean...

Wave | Loop-erased random walk | Critical exponent | Uniform spanning tree | Abelian sandpile | WALK | loop-erased random walk | SELF-ORGANIZED CRITICALITY | critical exponent | uniform spanning tree | STATISTICS & PROBABILITY | INFINITE VOLUME LIMIT | MODEL | wave | UNIFORM SPANNING FORESTS

Wave | Loop-erased random walk | Critical exponent | Uniform spanning tree | Abelian sandpile | WALK | loop-erased random walk | SELF-ORGANIZED CRITICALITY | critical exponent | uniform spanning tree | STATISTICS & PROBABILITY | INFINITE VOLUME LIMIT | MODEL | wave | UNIFORM SPANNING FORESTS

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 2015, Volume 22, Issue 1, pp. I - 66

We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central...

MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | MODELS | SELF-ORGANIZED CRITICALITY | SPANNING-TREES | POTENTIAL-THEORY | ABELIAN SANDPILE | DIMERS | GRAPHS

MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | MODELS | SELF-ORGANIZED CRITICALITY | SPANNING-TREES | POTENTIAL-THEORY | ABELIAN SANDPILE | DIMERS | GRAPHS

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 02/2015, Volume 22, Issue 1

The Abelian Sandpile Model (Dhar 1990) is a discrete diffusion process, defined on graphs, which serves as the standard model of selporganized criticality. One...

Harmonic functions on graphs | Transience class problem of sandpiles | Abelian sandpile model | MATHEMATICS | MATHEMATICS, APPLIED | TREES | Transience Class Problem of Sandpiles | MODELS | Abelian Sandpile Model

Harmonic functions on graphs | Transience class problem of sandpiles | Abelian sandpile model | MATHEMATICS | MATHEMATICS, APPLIED | TREES | Transience Class Problem of Sandpiles | MODELS | Abelian Sandpile Model

Journal Article

Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 10/2016, Volume 54, pp. 97 - 102

The recurrent states of the Abelian sandpile model (ASM) are those states that appear infinitely often. For this reason they occupy a central position in ASM...

sandpile group | recurrent states | level polynomial | Abelian sandpile model | graph decomposition

sandpile group | recurrent states | level polynomial | Abelian sandpile model | graph decomposition

Journal Article

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