Related papers: The Marcinkiewicz-type discretization theorems
This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
We consider the situation when a globally defined four-dimensional field system is separated on two entangled sub-systems by a dynamical (random) two-dimensional surface. The reduced density matrix averaged over ensemble of random surfaces…
Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
The aim of this paper is to investigate extremum problems with pay-off being the total variational distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures,…
We prove new Bernstein and Markov type inequalities in $L^p$ spaces associated with the normal and the tangential derivatives on the boundary of a general compact $C^\alpha$-domain with $1\leq \alpha\leq 2$. These estimates are also applied…
Entanglement entropy encodes important features of strongly interacting quantum many-body systems and gauge theories, but its analytical study is still limited to systems with high level of symmetry. This motivates the search for efficient…
I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach directly produces a discretisation for the evolution of the…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems…
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region…
In this paper, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advantages of…
We introduce a new basic model for independent and identical distributed sequence on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels with model uncertainty. Thanks to the well-defined…
We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…
It is known that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error measured in the square norm. In this paper we demonstrate how known results on universal sampling…