Related papers: Diffraction of compatible random substitutions in …
We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…
In this article we carefully distinguish the notion of bi-refringence (a polarization-dependent doubling in photon propagation speeds) from that of bi-metricity (where the two photon polarizations ``see'' two distinct metrics). We emphasise…
Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance. If a system has the infinite variance problem, one cannot estimate observables reliably even with an infinite number…
Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
In this paper we consider the Hilbert-Einstein-Dirac functional, whose critical points are pairs, metrics-spinors, that satisfy a system coupling the Riemannian and the spinorial part. Under some assumptions, on the sign of the scalar…
One of the important consequences of the Banach Fixed Point Theorem is Hutchinson's theorem which states the existence and uniqueness of fractals in complete metric spaces. The aim of this paper is to extend this theorem for semimetric…
We use generalised Zeckendorf representations of natural numbers to investigate mixing properties of symbolic dynamical systems. The systems we consider consist of bi-infinite sequences associated with so-called random substitutions. We…
This paper investigates the dimension theory of some families of continuous piecewise linear iterated function systems. For one family, we show that the Hausdorff dimension of the attractor is equal to the exponential growth rate obtained…
We study the optimal rectangular-discrepancy approximation of permutons by finite permutations. We transfer bounds from discrepancy theory to this more restricted setup. Moreover, we show that superlinear approximation can occur only for…
We prove an explicit formula for infinitely many convergents of Hurwitzian continued fractions that repeat several copies of the same constant and elements of one arithmetic progression, in a quasi-periodic fashion. The proof involves…
Let $E\subset \mathbb{R}^{n+1}$, $n\ge 1$, be a uniformly rectifiable set of dimension $n$. We show $E$ that has big pieces of boundaries of a class of domains which satisfy a 2-sided corkscrew condition, and whose connected components are…
The question of when the derived category of a ring satisfies Brown--Adams representability is revisited via studying the transfer of pure homological dimension along definable functors: it is shown that, for any ring, the pure global…
Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor $S(k,\omega)$ of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the…
We present a model of one-dimensional irreversible adsorption in which particles once adsorbed immediately shrink to a smaller size or expand to a larger size. Exact solutions for the fill factor and the particle number variance as a…
We examine optimal matchings or transport between two stationary random measures. It covers allocation from the Lebesgue measure to a point process and matching a point process to a regular (shifted) lattice. The main focus of the article…
A high-accuracy solution of the diffraction problem has become necessary for the treatment of certain special questions of statistical physics. This article reports the creation of a computer program that serves as an instrumental method of…
We construct a new class of infinite-dimensional diffusions taking values in a generalized Kingman simplex. Our model describes the temporal evolution of the relative frequencies of infinitely-many types which are "labeled" by an arbitrary…
In a recent paper, Lenz and Moody (arXiv:1111.3617) presented a method for constructing families of real solutions to the inverse problem for a given pure point diffraction measure. Applying their technique and discussing some possible…