Related papers: Weakly non-Gaussian formula for the Minkowski func…
Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to…
We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
In this research, Minkowski type functions which are constructed on certain probability distributions, are introduced. There are investigated differential, integral, and other properties of these functions.
Fractional Gaussian fields are scalar-valued random functions or generalized functions on an $n$-dimensional manifold $M$, indexed by a parameter $s$. They include white noise ($s = 0$), Brownian motion ($s=1, n=1$), the 2D Gaussian free…
We provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional magnetic resonance imaging) brain data. These papers…
Minkowski spacetime can be mapped by a series of projections in a higher-dimensional spacetime to a Euclidean space, constituting a process of Euclideanization shown here in detail for two dimensions. The result allows regularizations and…
In this paper, we obtain new results related to Minkowski fractional integral inequality using generalized k-fractional integral operator which is in terms of the Gauss hypergeometric function.
We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in one-dimensional marginal distributions of shear two-point…
Concerning the value distribution problem for generalized Gauss maps, we not only generalize Fujimoto's theorem to complete space-like stationary surfaces in Minkowski spacetime, but also estimate the upper bound of the number of…
Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of…
We study the effect of primordial non-Gaussianity on the development of large-scale cosmic structure using high-resolution N-body simulations. In particular, we focus on the topological properties of the "cosmic web", quantitatively…
In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
Invariance under finite conformal transformations in Minkowski space and the Wightman axioms imply strong locality (Huygens principle) and rationality of correlation functions, thus providing an extension of the concept of vertex algebra to…
In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
Cosmic shear - the weak gravitational lensing effect generated by fluctuations of the gravitational tidal fields of the large-scale structure - is one of the most promising tools for current and future cosmological analyses. The…
In this paper, we study the anisotropic Minkowski problem. It is a problem of prescribing the anisotropic Gauss-Kronecker curvature for a closed strongly convex hypersurface in Euclidean space as a function on its anisotropic normals in…
Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…