5,261 research outputs found
Limit theory for point processes in manifolds
Let , be i.i.d. random variables having values in an
-dimensional manifold and consider sums
, where is a real
valued function defined on pairs , with
and locally finite. Subject to
satisfying a weak spatial dependence and continuity condition, we show that
such sums satisfy weak laws of large numbers, variance asymptotics and central
limit theorems. We show that the limit behavior is controlled by the value of
on homogeneous Poisson point processes on -dimensional hyperplanes
tangent to . We apply the general results to establish the limit
theory of dimension and volume content estimators, R\'{e}nyi and Shannon
entropy estimators and clique counts in the Vietoris-Rips complex on
.Comment: Published in at http://dx.doi.org/10.1214/12-AAP897 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Growing Perfect Decagonal Quasicrystals by Local Rules
A local growth algorithm for a decagonal quasicrystal is presented. We show
that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling
layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to
form on the upper layer, successive 2D PPT layers can be added on top resulting
in a perfect decagonal quasicrystalline structure in bulk with a point defect
only on the bottom surface layer. Our growth rule shows that an ideal
quasicrystal structure can be constructed by a local growth algorithm in 3D,
contrary to the necessity of non-local information for a 2D PPT growth.Comment: 4pages, 2figure
Mathematics of random growing interfaces
We establish a thermodynamic limit and Gaussian fluctuations for the height
and surface width of the random interface formed by the deposition of particles
on surfaces. The results hold for the standard ballistic deposition model as
well as the surface relaxation model in the off-lattice setting. The results
are proved with the aid of general limit theorems for stabilizing functionals
of marked Poisson point processes.Comment: 12 page
Gaussian limits for multidimensional random sequential packing at saturation (extended version)
Consider the random sequential packing model with infinite input and in any
dimension. When the input consists of non-zero volume convex solids we show
that the total number of solids accepted over cubes of volume is
asymptotically normal as . We provide a rate of
approximation to the normal and show that the finite dimensional distributions
of the packing measures converge to those of a mean zero generalized Gaussian
field. The method of proof involves showing that the collection of accepted
solids satisfies the weak spatial dependence condition known as stabilization.Comment: 31 page
The fields of uniformly accelerated charges in de Sitter spacetime
The scalar and electromagnetic fields of charges uniformly accelerated in de
Sitter spacetime are constructed. They represent the generalization of the Born
solutions describing fields of two particles with hyperbolic motion in flat
spacetime. In the limit Lambda -> 0, the Born solutions are retrieved. Since in
the de Sitter universe the infinities I^+- are spacelike, the radiative
properties of the fields depend on the way in which a given point of I^+- is
approached. The fields must involve both retarded and advanced effects: Purely
retarded fields do not satisfy the constraints at the past infinity I^-.Comment: 5 pages, 3 figures, RevTeX; Slightly expanded version of the paper
published in Physical Review Letters. (The published version can be generated
from the same TeX source.); problem with the postscript fixe
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