Related papers: Gaussian random field's anisotropy using excursion…
The distribution of arrival directions of ultra-high energy cosmic rays may yield clues to their mysterious origin. We introduce a method of {\it invariant statistics} to analyze cosmic ray data which eliminates coordinate-dependent…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
Influence of weak uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field…
We investigate the asymptotic variance of Gaussian nodal excursions in the Euclidean space, focusing on the case where the spectral measure has incommensurable atoms. This study requires to establish fine recurrence properties in 0 for the…
Under certain conditions, the largest eigenvalue of a sample covariance matrix undergoes a well-known phase transition when the sample size $n$ and data dimension $p$ diverge proportionally. In the subcritical regime, this eigenvalue has…
The exquisitely measured maps of fluctuations in the Cosmic Microwave Background (CMB) present the possibility to test the principle of Statistical Isotropy (SI) of the Universe through systematic observable measures for non-Statistical…
The extraction of cosmological parameters from microwave background observations relies on specific assumptions about the statistical properties of the data, in particular that the p-point distributions of temperature fluctuations are…
Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use of these maps,…
Recent high precision cosmological observations have revealed several anomalies in the Cosmic Microwave Background (CMB), indicating possible violations of statistical isotropy (nSI). Typically, nSI in the CMB sky is studied in the harmonic…
We propose a set of statistics $S_q$ for detecting non-gaussianity in CMBR anisotropy data sets. These statistics are both simple and, according to calculations over a space of linear combinations of three-point functions, nearly optimal at…
We study various measures of weak lensing distortions in future surveys, taking into account the noise arising from the finite survey size and the intrinsic ellipticity of galaxies. We also consider a realistic redshift distribution of the…
The paper concerns a new statistical method for assessing dissimilarity of two random sets based on one realisation of each of them. The method focuses on shapes of the components of the random sets, namely on the curvature of their…
Any isotropy violating phenomena on cosmic microwave background (CMB) induces off-diagonal correlations in the two-point function. These correlations themselves can be used to estimate the underlying anisotropic signals. Masking due to…
Application of a Goodness--of--fit (GOF) statistic is an essential element of parameter estimation. We discuss the computation of GOF when estimating parameters from anisotropy measurements of the cosmic microwave background (CMB), and we…
We present a new approach for statistical inference on noise properties of CMB anisotropy data. We consider a Maximum Likelihood parametric estimator to recover the full dependence structure of the noise process. We also consider a…
When searching for deviations of statistical isotropy in CMB, a popular strategy is to write the two-point correlation function (2pcf) as the most general function of four spherical angles (i.e., two unit vectors) in the celestial sphere.…
We present a new analysis on how to distinguish between isotropic and anisotropic cosmological models based on tracking the angular displacements of a large number of distant quasars over an extended period of time, and then performing a…
Gaussianity of the cosmological perturbations in the universe is one of the key predictions of standard inflation, but it is violated by other models of structure formation such as topological defects. We present the first test of the…
Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our…
Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested…