Related papers: Abelian Sandpiles and the Harmonic Model
We numerically calculate the configurational entropy S_conf of a binary mixture of hard spheres, by using a perturbed Hamiltonian method trapping the system inside a given state, which requires less assumptions than the previous methods…
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…
In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy},…
We prove that the set of quadratic growths achievable by integer superharmonic functions on the $F$-lattice, a periodic subgraph of the square lattice with oriented edges, has the structure of an overlapping circle packing. The proof…
The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…
In \cite{J}, Jab\l o\'{n}ski proved that a piecewise expanding $C^{2}$ multidimensional Jab\l o\'{n}ski map admits an absolutely continuous invariant probability measure (ACIP). In \cite{BL}, Boyarsky and Lou extended this result to the…
We construct measure-preserving mappings from the $d$-dimensional unit cube to the $d$-dimensional unit ball and the compact rank one symmetric spaces, namely the $d$-dimensional sphere, the real, complex, and quaternionic projective…
We prove that the Abelian sandpile model on a random binary and binomial tree, as introduced in \cite{rrs}, is not critical for all branching probabilities $p<1$; by estimating the tail of the annealed survival time of a random walk on the…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
We compute Seidel's mirror map for abelian varieties by constructing the homogeneous coordinate rings from the Fukaya category of the symplectic mirrors. The computations are feasible as only linear holomorphic disks contribute to the…
An Abelian sandpile model is considered on the Husimi lattice of triangles with an arbitrary coordination number q. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived.
In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and…
We classify low-energy $\alpha$-harmonic maps from a closed non-spherical Riemannian surface $\Sigma$ of constant curvature to the round sphere via their bubble scales and centres. In particular we show that as $1<\alpha\downarrow 1$ and…
Let $(X,o)$ be a complex normal surface singularity. We fix one of its good resolutions $\widetilde{X}\to X$, an effective cycle $Z$ supported on the reduced exceptional curve, and any possible (first Chern) class $l'\in…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
It is shown that max-preserving maps (or join-morphisms) on the positive orthant in Euclidean $n$-space endowed with the component-wise partial order give rise to a semiring. This semiring admits a closure operation for maps that generate…
Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…
We provide a comprehensive view on the role of Abelian symmetry and stochasticity in the universality class of directed sandpile models, in context of the underlying spatial correlations of metastable patterns and scars. It is argued that…
Let $f$ be an holomorphic endomorphism of $\mathbb{P}^k$ and $\mu$ be its measure of maximal entropy. We prove an Almost Sure Invariance Principle for the systems $(\mathbb{P}^k,f,\mu)$. Our class $\cal{U}$ of observables includes the…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…