Related papers: Abelian sandpiles and algebraic models

We study the abelian sandpile model on the upper half plane, and reconsider the correlations of the four height variables lying on the boundary. For more convenience, we carry out the analysis in the dissipative (massive) extension of the…

By providing a suitable generalization of Newman's bijective correspondence known for cocommutative Hopf algebras, we prove that the category of cocommutative Hopf monoids in any abelian symmetric monoidal category is semi-abelian, once…

We compute the correlations of two height variables in the two-dimensional Abelian sandpile model. We extend the known result for two minimal heights to the case when one of the heights is bigger than one. We find that the most dominant…

Elliptic sheaves (which are related to Drinfeld modules) were introduced by Drinfeld and further studied by Laumon--Rapoport--Stuhler and others. They can be viewed as function field analogues of elliptic curves and hence are objects "of…

We solve a case of the Abelian Exponential-Algebraic Closedness Conjecture, a conjecture due to Bays and Kirby, building on work of Zilber, which predicts sufficient conditions for systems of equations involving algebraic operations and the…

The abelian sandpile model is a simple combinatorial model for critical behaviour which has the "abelian property" that the order in which we make moves does not change the final outcome of the game. This might seem to restrict the model's…

The symmetry properties which determine the critical exponents and universality classes in conservative sandpile models are identified. This is done by introducing a set of models, including all possible combinations of abelian vs.…

We study the height one, two, three, and four variables in the Abelian sandpile model. We argue that correlation functions along closed boundaries, as well as general conformal field theory principles, show that the four variables are not…

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 discuss some properties of the universality of the model.

The aim of the current work is to investigate structural properties of the sandpile group of a special class of self-similar graphs. More precisely, we consider Abelian sandpiles on Sierpinski gasket graphs and for the choice of normal…

In one-component abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multi-component models. The condition of associativity of the underlying abelian algebras impose nonlinear relations…

For a graph G, we construct two algebras, whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of…

A two-dimensional directed stochastic sandpile model is studied analytically with the use of directed Abelian algebras recently introduced by Alcaraz and V. Rittenberg [Phys. Rev. E {\bf 78}, 041126 (2008)]. Exact expressions for the…

Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers…

We consider a stochastic variant of the Abelian Sandpile Model (ASM) on a finite graph, introduced by Chan, Marckert and Selig. Even though it is a more general model, some nice properties still hold. We show that on a certain probability…

Asymptotic behavior (with respect to the number of trials) of symmetric generalizations of binomial distributions and their related entropies are studied through three examples. The first one derives from the q-exponential as a generating…

Two decades ago P. Martin and D. Woodcock made a surprising and prophetic link between statistical mechanics and representation theory. They observed that the decomposition numbers of the blob algebra (that appeared in the context of…

An Abelian sandpile model is considered on the Husimi lattice of square plaquettes. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived. The two-point correlation function for the…

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

The new notion of adjoint algebraic entropy of endomorphisms of Abelian groups is introduced. Various examples and basic properties are provided. It is proved that the adjoint algebraic entropy of an endomorphism equals the algebraic…