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The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…

In this paper, we extend our earlier result (see [Y-2008]) on the distribution of normalized zero-sets of random entire functions to random entire functions with small random perturbation.

We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To…

Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical…

We consider multivariate splines and show that they have a random feature expansion as infinitely wide neural networks with one-hidden layer and a homogeneous activation function which is the power of the rectified linear unit. We show that…

Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics of strongly mixing…

In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a…

A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…

It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and…

An explicit expression is derived for the distribution function of end-to-end vectors and for the mean square end-to-end distance of a flexible chain with excluded-volume interactions. The Hamiltonian for a flexible chain with weak…

Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…

The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our…

We study a discrete analogue of the classical multivariate Gaussian distribution. It is supported on the integer lattice and is parametrized by the Riemann theta function. Over the reals, the discrete Gaussian is characterized by the…

The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the…

Generalized linear models (GLM) are link function based statistical models. Many supervised learning algorithms are extensions of GLMs and have link functions built into the algorithm to model different outcome distributions. There are two…

We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal…

This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative…

The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…

We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have same distributions…

We develop a Galois theory of commutative rings under actions of finite inverse semigroups. We present equivalences for the definition of Galois extension as well as a Galois correspondence theorem. We also show how the theory behaves in…