Related papers: Spherical cap discrepancy of the Diamond ensemble

We investigate the ensemble inequivalence of the spherical spin glass model with nonlinear interactions of polynomial order $p$. This model is solved exactly for arbitrary $p$ and is shown to have first-order phase transitions between the…

We study lattice points in d-dimensional spheres, and count their number in thin spherical segments. We found an upper bound depending only on the radius of the sphere and opening angle of the segment. To obtain this bound we slice the…

In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such…

We present a theoretical framework to accurately calculate the location of the multicritical point in the phase diagram of spin glasses. The result shows excellent agreement with numerical estimates. The basic idea is a combination of the…

A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…

Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant…

The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…

We introduce a class of convex equivolume partitions. Expected star discrepancy results are compared for stratified samples under these partitions, including simple random samples. There are four main parts of our results. First, among…

We consider proper holomorphic maps of ball complements and differences in complex euclidean spaces of dimension at least two. Such maps are always rational, which naturally leads to a related problem of classifying rational maps taking…

We continue the study, begun in \cite{FA}, of the critical radius of embeddings, via deterministic spherical harmonics, of fixed dimensional spheres into higher dimensional ones, along with the associated problem of the distribution of the…

In this paper I uncover and explain---using contour integrals and residues---a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\'e scheme for…

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…

Let $ D$ be a bounded open subset of $\mathbb R^n$ with $|\partial D| < \infty$ and let $x_0 $ be a point of $D$. We introduce a new parameter, that we call Kuran gap of $\partial D$ w.r.t. $x_0$. Roughly speaking, this parameter, denoted…

Gaussian mixture model is very useful in many practical problems. Nevertheless, it cannot be directly generalized to non Euclidean spaces. To overcome this problem we present a spherical Gaussian-based clustering approach for partitioning…

We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Delaunay simplices, which are grouped together into finite…

We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are…

Let $A$ be abelian variety over the function field $K$ of a compact Riemann surface $B$. Fix a model $f \colon \mathcal{A} \to B$ of $A/K$ and a certain effective horizontal divisor $\DD \subset \mathcal{A}$. We give a sufficient condition…

We prove that a generic area-preserving diffeomorphism of a compact surface with non-empty boundary has an equidistributed set of periodic orbits. This implies that such a diffeomorphism has a dense set of periodic points, although we also…

In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $\phi$ to…

This paper develops a unified theory of natural superconvergence points for polynomial spline approximations to second-order elliptic problems. Beginning with the one-dimensional case, we establish that when a point $x_0$ is a local…