Related papers: Geography of local configurations

We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities…

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…

Consider the d-dimensional lattice Z^d where each vertex is ``open'' or ``closed'' with probability p or 1-p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth co-ordinates of v and w…

While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…

In this paper we consider sparsely random potentials in 5 or more dimensional cubic lattice and exhibit localized and extended states. We identify also the mobility edge for a class of potentials going to infinity at infinity. Our treatment…

Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…

We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…

Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.

We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply…

The initial value problem of the Zakharov system on two dimensional torus with general period is shown to be locally well-posed in the Sobolev spaces of optimal regularity, including the energy space. Proof relies on a standard iteration…

Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized…

We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…

We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size $L \times L$ sites when considering a plane (the crossing probability in a given direction), a cylinder…

Local convergence techniques have become a key methodology to study sparse random graphs. However, convergence of many random graph properties does not directly follow from local convergence. A notable, and important, such random graph…

We predict a generic mechanism of wave localization at an interface between uniform gauge fields, arising due to propagation-dependent phase accumulation similar to Aharonov-Bohm phenomenon. We realize experimentally a photonic mesh lattice…

We consider the lattice dynamics in the harmonic approximation for We consider the lattice dynamics in the harmonic approximation for a simple hypercubic lattice with arbitrary unit cell. The initial data are random according to a…

We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region it is necessary to inspect a…

We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy with the observation that for real-valued…

We give a sufficient condition on a family of radial parametrized long-range potentials for a compact local minimality of a given $d$-dimensional Bravais lattice for its total energy of interaction created by each potential. This work is…

We study excitations of the local field (locsitons) in nanoscale two-dimensional (2D) lattices of strongly interacting resonant atoms and various unusual effects associated with them. Locsitons in low-dimensional systems and the resulting…