Related papers: W-transforms: Uniformity-preserving transformation…
We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for…
Stochastic large scale interacting systems can be studied via the observables, i.e. functions on the underlying configuration space. In our previous article, we introduced the concept of uniform functions, which are suitable class of…
The copula representations for conditionally independent random variables and the distribution properties of order statistics of these random variables are studied.
The copulas of random vectors with standard uniform univariate margins truncated from the right are considered and a general formula for such right-truncated conditional copulas is derived. This formula is analytical for copulas that can be…
Probability density estimation is a central task in statistics. Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions…
In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…
The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm…
Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…
The processes of production and subsequent decay of W- and Z-bosons in $e^+ e^-$ collisions are considered in a recently proposed modified perturbation theory (PT), based on a direct expansion of probabilities instead of amplitudes. In such…
Several distributions and families of distributions are proposed to model skewed data, think, e.g., of skew-normal and related distributions. Lambert W random variables offer an alternative approach where, instead of constructing a new…
We present groupoid morphisms as an algebraic structure for nonautonomous dynamics, as well as a generalization of group morphisms, which describe classic dynamical systems. We introduce the structure of cotranslations, as a specific kind…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…
The distribution function of the sum $Z$ of two standard normally distributed random variables $X$ and $Y$ is computed with the concept of copulas to model the dependency between $X$ and $Y$. By using implicit copulas such as the Gauss- or…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
Our article addresses the problem of flexibly estimating a multivariate density while also attempting to estimate its marginals correctly. We do so by proposing two new estimators that try to capture the best features of mixture of normals…
Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation…
Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this…
We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…