Related papers: Probabilistic Lower Bounds for the Discrepancy of …
In this paper we study uniform distribution properties of digital sequences over a finite field of prime order. In 1998 it was shown by Larcher that for almost all $s$-dimensional digital sequences the star discrepancy $D_N^\ast$ satisfies…
By collecting distances from the literature, a set of 73 planetary nebulae with mean distances of high accuracy is derived. This sample is used for recalibration of the mass-radius relationship, used by many statistical distance methods. An…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
An accurate determination of the Hubble constant remains a puzzle in observational cosmology. The possibility of a new physics has emerged with a significant tension between the current expansion rate of our Universe measured from the…
Current measurements of the Hubble constant $H_0$ on scale less than $\sim100$ Mpc appear to be controversial, while the observations made at high redshift seem to provide a relatively low value. On the other hand, the Hubble expansion is…
In this paper we extend a result of Levin, who proved a lower bound on the star discrepancy of generalized Halton sequences in positive integer bases, to rational bases.
It is known that there is a constant $c>0$ such that for every sequence $x_1, x_2,\ldots$ in $[0,1)$ we have for the star discrepancy $D^{*}_N$ of the first $N$ elements of the sequence that $N D^{*}_N\geq c\cdot \log N$ holds for…
Considerable progress has been made in determining the Hubble constant over the past two decades. We discuss the cosmological context and importance of an accurate measurement of the Hubble constant, and focus on six high-precision…
In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap…
A new lower bound on the average reconstruction error variance of multidimensional sampling and reconstruction is presented. It applies to sampling on arbitrary lattices in arbitrary dimensions, assuming a stochastic process with constant,…
Accurate distances to pulsars can be used for a variety of studies of the Galaxy and its electron content. However, most distance measures to pulsars have been derived from the absorption (or lack thereof) of pulsar emission by Galactic HI…
We consider a certain equidistributed sequence of rational numbers constructed from the primes. In particular, we determine the sharp convergence rate for the star discrepancy of said sequence. Our arguments are based on well-known…
Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The methods compared are Monte Carlo with pseudo-random numbers, Latin Hypercube Sampling,…
The $L_{\infty}$ star discrepancy is a measure for the regularity of a finite set of points taken from $[0,1)^d$. Low discrepancy point sets are highly relevant for Quasi-Monte Carlo methods in numerical integration and several other…
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…
We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.
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 update constraints on cosmic opacity by combining recent SN Type Ia data compilation with the latest measurements of the Hubble expansion at redshifts between 0 and 2. The new constraint on the parameter $\epsilon$ parametrising…
Let $\mathcal{S}$ be a finite set of integer points in $\mathbb{R}^d$, which we assume has many symmetries, and let $P\in\mathbb{R}^d$ be a fixed point. We calculate the distances from $P$ to the points in $\mathcal{S}$ and compare the…
In this paper we propose an acceptance-rejection sampler using stratified inputs as diver sequence. We estimate the discrepancy of the points generated by this algorithm. First we show an upper bound on the star discrepancy of order…