Related papers: Probabilistic Lower Bounds for the Discrepancy of …
We prescribe the minimal set of experimental data and parameters that should be reported for random-laser experiments and models. This prescript allows for a quantitative comparison between different experiments, and for a criterion whether…
We have carefully studied how local measurements of the Hubble constant, $H_0$, can be influenced by a variety of different parameters related to survey geometry, depth, and size, as well as observer position in space. Our study is based on…
We consider the problem of estimating $\mathbb{E} [f(U^1, \ldots, U^d)]$, where $(U^1, \ldots, U^d)$ denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving…
Light from `point sources' such as supernovae is observed with a beam width of order of the sources' size - typically less than 1 AU. Such a beam probes matter and curvature distributions that are very different from coarse-grained…
We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…
Following a result of D.~Bylik and M.T.~Lacey from 2008 it is known that there exists an absolute constant $\eta>0$ such that the (unnormalized) $L^{\infty}$-norm of the three-dimensional discrepancy function, i.e, the (unnormalized) star…
Simplex slicing (Webb, 1996) is a sharp upper bound on the volume of central hyperplane sections of the regular simplex. We extend this to sharp bounds in the probabilistic framework of negative moments, and beyond, of centred log-concave…
New distances, larger than previous ones, have been obtained for M 31 and M 81 based on the geometrical zero-point of the Cepheid Period-luminosity relation provided by the HIPPARCOS satellite. By combining them with independent…
Consider $S$, a set of $n$ points chosen uniformly at random and independently from the unit hypercube of dimension $t>2$. Order $S$ by using the Cartesian product of the $t$ standard orders of $[0,1]$. We determine a constant $\bar x(t)<e$…
The dispersion measure-redshift relation of fast radio bursts (FRBs) provides a valuable cosmological probe for constraining the Hubble constant, offering an independent measurement that could help resolve the ongoing Hubble tension. In…
We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
Point lens microlensing events with impact parameter close to the source stellar radius allow the observer to study the surface brightness profile of the lensed source. We have examined the effect of photospheric star spots on multicolour…
The success of present and future cosmological studies is tied to the ability to detect discrepancies in complex data sets within the framework of a cosmological model. Tensions caused by the presence of unknown systematic effects need to…
We use a sample of 45 core collapse supernovae detected with the Advanced Camera for Surveys on-board the Hubble Space Telescope to derive the core collapse supernova rate in the redshift range 0.1<z<1.3. In redshift bins centered on…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
Stellar evolution models are a cornerstone of young star astrophysics, which necessitates that they yield accurate and reliable predictions of stellar properties. Here, I review the current performance of stellar evolution models against…
In this paper, we study the cosmological constraints from the measurements of Hubble parameters---$H(z)$ data. Here, we consider two kinds of $H(z)$ data: the direct $H_0$ probe from the Hubble Space Telescope (HST) observations of Cepheid…
We perform a number of inter-related cosmographic fits to the legacy05 and gold06 supernova datasets. We pay particular attention to the influence of both statistical and systematic uncertainties, and also to the extent to which the choice…
Present day estimates of the Hubble constant based on Cepheids and on the cosmic microwave background radiation are uncertain by roughly 10% (on the conservative assumption that the universe may not be PERFECTLY flat). Gravitational lens…