Related papers: Characterizing immutable sandpiles: A first look
A noncommutative polynomial is stable if it is nonsingular on all tuples of matrices whose imaginary parts are positive definite. In this paper a characterization of stable polynomials is given in terms of strongly stable linear matrix…
The divisible sandpile starts with i.i.d. random variables ("masses") at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an attempt to make all masses at most 1. The process…
A map which is non-orientable or has non-empty boundary has a canonical double cover which is orientable and has empty boundary. The map is called stable if every automorphism of this cover is a lift of an automorphism of the map. This note…
Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex…
We show that the patterns in the Abelian sandpile are stable. The proof combines the structure theory for the patterns with the regularity machinery for non-divergence form elliptic equations. The stability results allows one to improve…
Experimental observation of a new mechanism of sandpile formation is reported. As a steady stream of dry sand is poured onto a horizontal surface, a pile forms which has a thin river of sand on one side flowing from the apex of the pile to…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
Roughly speaking, a conic bundle is a surface, fibered over a curve, such that the fibers are conics (not necessarily smooth). We define stability for conic bundles and construct a moduli space. We prove that (after fixing some invariants)…
After the introduction of sandpile model a number of different variants have been studied. In most of these models sand particles are indistinguishable. Here we have painted the sand particles using a few distinct colors, and restrict them…
We carry out a survey on curves defined over finite fields that are Diophantine stable; that is, with the property that the set of points of the curve is not altered under a proper field extension. First, we derive some general results of…
We consider a noncommutative scalar field with a covariantly constant noncommutative parameter in a curved space-time background. For a potential as a noncommutative polynomial it is shown that the stability conditions are unaffected by the…
We introduce a one-dimensional sandpile model with $N$ different particle types and an infinitesimal driving rate. The parameters for the model are the N^2 critical slopes for one type of particle on top of another. The model is trivial…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
We start up the study of the stability of general graph pairs. This notion is a generalization of the concept of the stability of graphs. We say that a pair of graphs $(\Gamma,\Sigma)$ is stable if $Aut(\Gamma\times\Sigma) \cong…
We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate $1$, sending two of its particles to neighbouring…
We prove that the space of complex irreducible polynomials of degree $d$ in $n$ variables satisfies two forms of homological stability: first, its cohomology stabilizes as $d$ increases, and second, its compactly supported cohomology…
In this paper we introduce a new property for normed algebras. This property which we call it stability, plays a key role in the studying of the theory of almost multiplier maps. In this note we study some of the basic properties of this…
We compute the sandpile groups of families of planar graphs having a common weak dual by evaluating the indeterminates of the critical ideals of the weak dual at the lengths of the cycles bounding the interior faces. This method allow us to…
Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with the…
Capillary forces significantly affect the stability of sandpiles. We analyze the stability of sandpiles with such forces, and find that the critical angle is unchanged in the limit of an infinitely large system; however, this angle is…