相关论文: Geography of local configurations
The cutoff phenomenon describes a sharp transition in the convergence of a Markov chain to equilibrium. In recent work, the authors established cutoff and its location for the stochastic Ising model on the $d$-dimensional torus $(Z/nZ)^d$…
We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in analogy to the well-studied case of random Schroedinger…
We show, through analytical theory and rigorous numerical calculations, that optical binding can organize a collection of particles into stable one-dimensional lattice. This lattice, as well as other optically-bound structures, are shown to…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…
Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…
Let $X$ be a smooth projective variety of dimension $n\geq 2$. It is shown that a finite configuration of points on $X$ subject to certain geometric conditions possesses rich inner structure. On the mathematical level this inner structure…
Consider $n$ $d$-dimensional vectors with iid entries from a lattice distribution $X$. We show that the probability that all distances between them are equal is asymptotically \[ C_n\cdot\frac{1}{d^{(m-1)/2}} \quad \text{for} \quad d \to…
For a dynamical system, we study the set of points $\cal W$ whose orbit approximates any chosen point at certain specified rates. Our basic setting is that of left shift acting on topological Markov chains endowed with a local weak Gibbs…
We show that the spontaneous breaking of center symmetry can be avoided on a $L^2\times 1^2$ lattice with the appropriate choice of twisted boundary conditions. In order for this to work it is crucial that the twisted boundary conditions…
Under the hypothesis of no topological structure below a certain scale, we prove that any U(1) lattice configuration corresponds to a classical U(1) gauge field with zero local field strength; i.e. any local representative of the pullback…
A natural two-metric formalism, generated by the world function of the space-time, is used. This circumstance admits one to localize the relative gravitational field, which is described by a tensor.
We consider branching random walks on the Euclidean lattice in dimensions five and higher. In this non-Markovian setting, we first obtain a relationship between the equilibrium measure and Green's function, in the form of an approximate…
A model of lightning that captures the propagation of lightning channels on an irregular lattice is developed. The irregular lattice allows us to capture large two-dimensional systems (2 km x 2 km), while allowing grid refinement (on the…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice $\mathbb{Z}^{2}$, gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. We consider the limit of deep one- and two-dimensional (1D and 2D) lattices in this system, featuring finite bandgaps separated by…
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…