相关论文: A Kiefer--Wolfowitz comparison theorem for Wicksel…
The behavior of slow-fast diffusions as the separation of scale diverges is a well-studied problem in the literature. In this short paper, we revisit this problem and obtain a new proof of existing strong quantitative convergence estimates…
We explore the sensitivity of weak lensing observables to the expansion history of the universe and to the growth of cosmic structures, as well as the relative contribution of both effects to constraining cosmological parameters. We utilize…
We present detailed calculations of the magnification distribution, including both weak and strong lensing, using very recent solutions of the Dyer-Roeder (1973) equation for light propagation in a inhomogeneous universe with a cosmological…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
We show that if an essentially arbitrary sequence supported on an interval containing $x$ integers, is convolved with a tiny Siegel-Walfisz-type sequence supported on an interval containing $\exp((\log x)^{\varepsilon})$ integers then the…
We study the distribution of a general class of asymptoticallylinear statistics which are symmetric functions of $N$ independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a…
If dark matter interacts too strongly with nuclei, it could be slowed to undetectable speeds in Earth's crust or atmosphere before ever reaching a detector. For sub-GeV dark matter, analytic approximations appropriate for heavier dark…
On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new…
We review Gordon's optical metric and the transport equations for the amplitude and polarization of a geometrical optics wave traveling in a gravity field. We apply the theory to the FLRW cosmologies by associating a refraction index with…
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
We study the distribution of dark matter in the Draco dwarf spheroidal galaxy by modelling the moments of the line-of-sight velocity distribution of stars obtained from new velocity data of Wilkinson et al. The luminosity distribution is…
The Dvoretzky--Kiefer--Wolfowitz (DKW) inequality says that if $F_n$ is an empirical distribution function for variables i.i.d.\ with a distribution function $F$, and $K_n$ is the Kolmogorov statistic $\sqrt{n}\sup_x|(F_n-F)(x)|$, then…
The Fermat principle is advocated to be a convenient tool to analyze the light propagation in a curved space time. It is shown that in the weak deflection regime the light ray trajectories can be systematically described by applying the…
Determining the dark matter (DM) mass is of paramount importance for understanding dark matter. We present a novel parametrization of the DM speed distribution which will allow the DM mass to be accurately measured using data from Weakly…
The matter distribution of the Universe can be mapped through the weak gravitational lensing (WL) effect: small distortions of the shapes of distant galaxies, which reflects the inhomogeneity of the cosmic density field. The most dominant…
Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$.…
By combining the definition of the Wigner distribution function (WDF) and the matrix method of optical system modeling, we can evaluate the transformation of the former in centered systems with great complexity. The effect of stops and lens…
The article deals with a classical inverse problem: the computation of the refractive index of a medium from ultrasound time-of-flight (TOF) measurements. This problem is very popular in seismics but also for tomographic problems in…
In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the stochastic nature of the inequality, the relation between the exponents of intgrability is modified. This modification can be understood as a…
The Lorentz covariant theory of propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses is constructed. The theory is based on the Lienard-Wiechert…