Related papers: A transference inequality for rational approximati…
We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and V\'azquez, where the pressure is obtained as a Riesz potential associated to the density.…
We obtain a Fourier dimension estimate for sets of exact approximation order introduced by Bugeaud for certain approximation functions $\psi$. This Fourier dimension estimate implies that these sets of exact approximation order contain…
The Langevin algorithms are frequently used to sample the posterior distributions in Bayesian inference. In many practical problems, however, the posterior distributions often consist of non-differentiable components, posing challenges for…
Ratios of quadratic forms in correlated normal variables which introduce noncentrality into the quadratic forms are considered. The denominator is assumed to be positive (with probability 1). Various serial correlation estimates such as…
Gallagher's theorem is a sharpening and extension of the Littlewood conjecture that holds for almost all tuples of real numbers. We provide a fibre refinement, solving a problem posed by Beresnevich, Haynes and Velani in 2015. Hitherto,…
We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous…
We determine when the equidistribution property for possibly moving targets holds for a rational function of degree more than one on the projective line over an algebraically closed field of any characteristic and complete with respect to a…
In 1998, Kleinbock & Margulis established a conjecture of V.G. Sprindzuk in metrical Diophantine approximation (and indeed the stronger Baker-Sprindzuk conjecture). In essence the conjecture stated that the simultaneous homogeneous…
This article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context. In the first part of our work we find the optimal constants in the Khintchine inequality for random vectors…
A bilinear inequality of Geba, Greenleaf, Iosevich, Palsson, and Sawyer for the Fourier transform is shown to be equivalent to a simpler linear inequality, and the range of exponents is extended. Related mixed-norm inequalities are…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
We give bounds on the rate of convergence to equilibrium of the symmetric simple exclusion process in $\Z^d$. Our results include the existent results in the literature. We get better bounds and larger class of initial states via a unified…
In this article we derive an approximation inequality for continued radicals, generalizing an inequality of Herschfeld for continued square roots to arbitrary radicals, which is useful in exploring convergence issues and obtaining…
Dyadic shifts of point distributions in the multi-dimensional unit cube are considered as a randomization. Explicit formulas for the discrepancies of such randomized distributions are given in the paper in terms of Rademacher functions.…
[B{\l}aszczyszyn, Yogeshwaran and Yukich (2019)] established central limit theorems for geometric statistics of point processes having fast decay dependence. As limit theorems are of limited use unless we understand their errors involved in…
A method is suggested for treating the well-known deficiency in the use of Pade approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.