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ABELIAN SANDPILES
, 1991
"... A class of models for self organized criticality can be described in terms of a large Abelian group. Several exact results follow, including the existence of a unique nontrivial configuration representing the identity element. ..."
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Cited by 14 (0 self)
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A class of models for self organized criticality can be described in terms of a large Abelian group. Several exact results follow, including the existence of a unique nontrivial configuration representing the identity element.
Abelian sandpile model on the Bethe lattice
 J. Phys. A: Math. Gen
, 1990
"... Abelian sandpile model on the Bethe lattice ..."
On the Avalanchefiniteness of Abelian Sandpiles
, 2008
"... We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanchefinite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also computationally feasible since it involves no greater than O ( N 3) a ..."
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We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanchefinite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also computationally feasible since it involves no greater than O ( N 3
APOLLONIAN STRUCTURE IN THE ABELIAN SANDPILE
, 2012
"... We state a conjecture relating integervalued superharmonic functions on Z² to an Apollonian circle packing of R². The conjecture is motivated by the Abelian sandpile process, which evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing on ..."
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Cited by 3 (2 self)
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We state a conjecture relating integervalued superharmonic functions on Z² to an Apollonian circle packing of R². The conjecture is motivated by the Abelian sandpile process, which evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing
ABELIAN SANDPILES AND THE HARMONIC MODEL
, 2009
"... We present a construction of an entropypreserving equivariant surjective map from the ddimensional critical sandpile model to a certain closed, shiftinvariant subgroup of T Zd (the ‘harmonic model’). A similar map is constructed for the dissipative abelian sandpile model and is used to prove un ..."
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Cited by 8 (3 self)
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We present a construction of an entropypreserving equivariant surjective map from the ddimensional critical sandpile model to a certain closed, shiftinvariant subgroup of T Zd (the ‘harmonic model’). A similar map is constructed for the dissipative abelian sandpile model and is used to prove
The abelian sandpile and related models
 Physica A
, 1999
"... The Abelian sandpile model is the simplest analytically tractable model of selforganized criticality. This paper presents a brief review of known results about the model. The abelian group structure of the algebra of operators allows an exact calculation of many of its properties. In particular, wh ..."
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Cited by 29 (0 self)
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The Abelian sandpile model is the simplest analytically tractable model of selforganized criticality. This paper presents a brief review of known results about the model. The abelian group structure of the algebra of operators allows an exact calculation of many of its properties. In particular
Convergence of the abelian sandpile
 Duke Math. J
"... Abstract. The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice Zd, in which sites with at least 2d chips topple, distributing 1 chip to each of their neighbors in the lattice, until no more topplings are possible. From an ini ..."
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Cited by 6 (1 self)
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Abstract. The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice Zd, in which sites with at least 2d chips topple, distributing 1 chip to each of their neighbors in the lattice, until no more topplings are possible. From
The Abelian Sandpile Model on an Infinite Tree
, 2008
"... We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting features of selforganized criticality. ..."
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Cited by 16 (4 self)
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We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting features of selforganized criticality.
Abelian sandpile models
, 2003
"... Infinite volume limit for the stationary distribution of ..."
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Cited by 4 (0 self)
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Infinite volume limit for the stationary distribution of
Results 1  10
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