Related papers: Harmonic measure and "locally flat" domains
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
This paper concerns harmonic measure on the domains that arise when infinitely many disjoint closed discs are removed from the unit disc. It investigates which configurations of discs are unavoidable for Brownian motion, and obtains…
The classical and the fractional Laplacians exhibit a number of similarities, but also some rather striking, and sometimes surprising, structural differences. A quite important example of these differences is that any function (regardless…
This paper investigates the properties of trajectories in harmonic oscillator systems equipped with a point, absolutely continuous, or singular measure. As demonstrated in [30], infinite-dimensional linear flows of countable oscillator…
Vacuum fluctuations can obscure the detection signal of the measurement of the smallest quantum objects like single particles seemingly implying a fundamental limit to measurement accuracy. However, as we show relativistic invariance…
In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…
Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set…
A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…
We examine domain-valued maxitive measures defined on the Borel subsets of a topological space. Several characterizations of regularity of maxitive measures are proved, depending on the structure of the topological space. Since every…
Let $\Omega^+\subset\mathbb R^{n+1}$ be a bounded $\delta$-Reifenberg flat domain, with $\delta>0$ small enough, possibly with locally infinite surface measure. Assume also that $\Omega^-= \mathbb R^{n+1}\setminus \overline{\Omega^+}$ is an…
Local Asymptotic Normality (LAN) property for fractional Gaussian noise under high-frequency observations is proved with a non-diagonal rate matrix depending on the parameter to be estimated. In contrast to the LAN families in the…
Using only linear interactions and a local parity measurement we show how entanglement can be detected between two harmonic oscillators. The scheme generalizes to measure both linear and non-linear functionals of an arbitrary oscillator…
Let $T$ be a topological space admitting a compatible proper metric, that is, a locally compact, separable and metrisable space. Let $\mathcal{M}^T$ be the non-empty set of all proper metrics $d$ on $T$ compatible with its topology, and…
We reduce the problem of proving decay estimates for viscosity solutions of fully nonlinear PDEs to proving analogous estimates for solutions of one-dimensional ordinary differential inequalities. Our machinery allow the ellipticity to…
We consider the volume expansion of the Blaschke metric, which is a projectively invariant metric on a strictly convex domain in a locally flat projective manifold. When the boundary is even dimensional, we express the logarithmic…
Dynamics of cylindrical and spherical relativistic domain walls is investigated with the help of a new method based on Taylor expansion of the scalar field in a vicinity of the core of the wall. Internal oscillatory modes for the domain…
It will be established that the mean oscillation of a function on a metric-measure space $X\times Y$ will be small if its mean oscillation on $X$ is small and some simple information on its (partial $Y$) upper-gradient is given.…
We study the stochastic stability in the zero-noise limit from a quantitative point of view. We consider smooth expanding maps of the circle, perturbed by additive noise. We show that in this case the zero-noise limit has a quadratic speed…
Motivated by connections to random matrices, Littlewood-Richardson coefficients and tilings, we study random discrete concave functions on an equilateral lattice. We show that such functions having a periodic Hessian of a fixed average…
We measure the cosmological matter density by observing the positions of baryon acoustic oscillations in the clustering of galaxies in the Sloan Digital Sky Survey (SDSS). We jointly analyse the main galaxies and LRGs in the SDSS DR5…