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We study the problem of comparing ageing patterns of the lifetime of k-out-of-n systems. Mathematically, this reduces to being able to decide about a stochastic ordering relationship between different order statistics. We discuss such…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
Dark matter N-body simulations suggest that the velocity distribution of dark matter is anisotropic. In this work we employ a mass model for the Milky Way whose parameters are determined from a fit to kinematical data. Then we adopt an…
We study approximations of reflected It\^o diffusions on convex subsets $D$ of $\Rd$ by solutions of stochastic differential equations with penalization terms. We assume that the diffusion coefficients are merely measurable (possibly…
We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least…
I propose a method to fit the probability distribution function (hereafter PDF) of the large scale density field rho, motivated by a Lagrangian version of the continuity equation. It consists in applying the Edgeworth expansion to the…
We investigate stellar mass and central dark matter density profiles of photometric luminous red galaxies with stellar masses of $\sim10^{10}-10^{12}M_\odot$ using weak gravitational lensing measurements from the Hyper Suprime-Cam Subaru…
We prove a Harnack inequality for positive solutions of a parabolic equation with slow anisotropic spatial diffusion. After identifying its natural scalings, we reduce the problem to a Fokker-Planck equation and construct a self-similar…
Dark matter currents in the large-scale structure give rise to gravitomagnetic terms in the metric, which affect the light propagation. Corrections to the weak lensing power spectrum due to these gravitomagnetic potentials are evaluated by…
In this paper we consider a distributed stochastic optimization problem without the gradient/subgradient information for the local objective functions, subject to local convex constraints. The objective functions may be non-smooth and…
One of the main goals of modern cosmology remains to summon up a self consistent policy, able to explain, in the framework of the Einstein's theory, the cosmic speed up and the presence of Dark Matter in the Universe. Accordingly to the…
We examine the Velocity Distribution Function (VDF) in dark matter halos from Milky Way to cluster mass scales. We identify an empirical model for the VDF with a wider peak and a steeper tail than a Maxwell--Boltzmann distribution, and…
Dark energy models which alter the relative scaling behavior of dark energy and matter could provide a natural solution to the cosmic coincidence problem - why the densities of dark energy and dark matter are comparable today. A generalized…
The drift and diffusion coefficients of the inhomogeneous multi-mass degenerate Landau equation are computed to describe the self-induced resonant relaxation of a discrete self-gravitating quasi-Keplerian razor-thin axisymmetric disc…
The scattering of sub-GeV dark matter in direct detection experiments happens at characteristic wavelengths comparable or larger than the interparticle spacing. Collective effects in the target material must therefore be accounted for when…
An approximation is derived for a Langevin equation with distribution-dependent potential and state-dependent, randomly fast oscillation. By some estimates and a diffusion approximation the limiting equation is shown to be…
Weak gravitational lensing, resulting from the bending of light due to the presence of matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It stands as a…
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption…
We consider the Kelvin-Voigt model for the viscoelasticity, and prove a Carleman estimate for functions without compact supports. Then we apply the Carleman estimate to prove the Lipschitz stability in determining a spatial varying function…
The effective field theory of dark energy predicts a possible time variation of the propagation speed of gravitational waves (GW) which could be tested with multimessenger astronomy. For this purpose we derive the relation between the…