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We study the minimal sample size N=N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound…
Weak gravitational lensing observations probe the spectrum and evolution of density fluctuations and the cosmological parameters which govern them. The non-linear evolution of large scale structure produces a non-Gaussian signal which is…
Every signal propagating through the universe is at least weakly lensed by the intervening gravitational field. In some situations, wave-optics phenomena (diffraction, interference) can be observed as frequency-dependent modulations of the…
In this work we are concerned with the study of the strong order of convergence in the averaging principle for slow-fast systems of stochastic evolution equations in Hilbert spaces with additive noise. In particular the stochastic…
We estimate density and regression functions for weak dependant datas. Using an exponential inequality obtained by Dedecker and Prieur and in a previous article of the author, we control the deviation between the estimator and the function…
The velocity distribution of dark matter is supposed to be isotropic Maxwell- Boltzmann distribution in most cases, however, its anisotropy is suggested by some simulations. We investigate conditions to give constraints on the anisotropy…
We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation…
Weak gravitational lensing on a cosmological scales can provide strong constraints both on the nature of dark matter and the dark energy equation of state. Most current weak lensing studies are restricted to (two-dimensional) projections,…
Weak gravitational lensing (WL) causes distortions of galaxy images and probes massive structures on large scales, allowing us to understand the late-time evolution of the Universe. One way to extract the cosmological information from WL is…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
A cosmological model with a gravitational Lagrangian $L_g(R)\propto R+A R^n$ is set up to account for the presently observed re-acceleration of the universe. The evolution equation for the scale factor $a$ of the universe is analyzed in…
We derive the Wick theorem for the q-Exponential distribution. We use the theorem to derive an algorithm for finding parameters of the correlation matrix of q-Exponentialy distributed random variables given empirical spectral moments of the…
The small but measurable effect of weak gravitational lensing on the cosmic microwave background radiation provide information about the large-scale distribution of matter in the universe. We use the all sky distribution of matter, as…
We present a new harmonic-domain approach for extracting morphological information, in the form of Minkowski Functionals (MFs), from weak lensing (WL) convergence maps. Using a perturbative expansion of the MFs, which is expected to be…
We propose an interesting mechanism to reconcile the recent experiments of the Michelson-Morley type and slowdown of the velocity of light in dark matter with a fractional electric charge when the index of refraction of dark matter depends…
I show how weak gravitational lensing can be used to image the 3-D mass distribution in the Universe. An inverse relation to the lensing equation, relating the lensing potential evaluated at each source to the full 3-D Newtonian potential,…
Understanding the nature of dark matter is among the top priorities of modern physics. However, due to its inertness, detecting and studying it directly in terrestrial experiments is extremely challenging. Numerical N-body simulations…
In this paper we study second order stochastic differential equations with measurable and density-distribution dependent coefficients. Through establishing a maximum principle for kinetic Fokker-Planck-Kolmogorov equations with…
We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…
A lower bound on unbiased estimates of wavefront errors (WFE) is presented for the linear regime of small perturbation and active control of a high-contrast region (dark hole). Analytical approximations and algorithms for computing the…