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pile (5) 5
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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
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 7/2019, Volume 138, Issue 1, pp. 361 - 403
Journal Article
by Kim, S and Wang, YT
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Journal Article
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