Related papers: Variations on theorems of Mertens
The work studies some Difference equations, which are connected with Mejer's function.
Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of…
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
In this short note we give counterexamples to several results related to extension theorems published recently.
We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler-Lagrange equation we receive a result analogous to Bernstein's theorem on non-parametric minimal surfaces.…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
This paper is a contribution to the study of extensions of arbitrary models of ZF (Zermelo-Fraenkel set theory), with no regard to countability or well-foundedness of the models involved. We present some new constructions of certain types…
Starting with the Fourier integral theorem, we present natural Monte Carlo estimators of multivariate functions including densities, mixing densities, transition densities, regression functions, and the search for modes of multivariate…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
We study representations of a random variable $\xi$ as an integral of an adapted process with respect to the Lebesgue measure. The existence of such representations in two different regularity classes is characterized in terms of the…
This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
In this paper we consider a sum of modified Bessel functions of the first kind of which particular case is used in the study of Kanter's sharp modified Bessel function bound for concentrations of some sums of independent symmetric random…
We derive new bounds of fewnomial type for the number of real solutions to systems of polynomials that have structure intermediate between fewnomials and generic (dense) polynomials. This uses a modified version of Gale duality for…
A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by…
The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.
The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to…
Understanding how torsion theories are described and constructed is crucial to the study of torsion theory. Mutations of torsion theories have been studied as a method of constructing another torsion theory from a given one. We have already…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
In this work, we study the validity of Entropy inequalities under decorrelation assumptions at large-scales, and also we study the problem of Weighted Meyers estimate in perforated domains. As a consequence, we obtain the hypercontractivity…