Related papers: Relation between asymptotic $L_p$-convergence and …
We estimate the $L^{p}$ norms of the discrepancy between the volume and the number of integer points in $r\Omega-x$, a dilated by a factor $r$ and translated by a vector $x$ of a convex body $\Omega$ in $\mathbb{R}^{d}$ with smooth boundary…
We consider the discrepancy of the integer lattice with respect to the collection of all translated copies of a dilated convex body having a finite number of flat, possibly non-smooth, points in its boundary. We estimate the $L^{p}$ norm of…
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the…
In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalises expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain…
In this paper, we introduce the concept of general $L_p$ projection body and general $L_p$ centroid body of general measures with positive homogeneity density function, and prove the corresponding extreme inequalities. Meanwhile, we also…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
This paper presents the asymptotic analysis of random lattices in high dimensions to clarify the distance properties of the considered lattices. These properties not only indicate the asymptotic value for the distance between any pair of…
By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…
Intrinsic $L_p$ metrics are defined and shown to satisfy a dimension--free bound with respect to the Hausdorff metric.
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
We introduce p-equivalence by asymptotic probabilities, which is a weak almost-equivalence based on zero-one laws in finite model theory. In this paper, we consider the computational complexities of p-equivalence problems for regular…
We discuss the relationship between ratio asymptotics for general orthogonal polynomials and the asymptotics of the associated Bergman shift operator. More specifically, we consider the case in which a measure is supported on an infinite…
We prove sharp asymptotic estimates for the gradient of positive solutions to certain nonlinear $p$-Laplace equations in Euclidean space by showing symmetry and uniqueness of positive solutions to associated limiting problems.
We find the best asymptotic lower bounds for the coefficient of the leading term of the $L_1$ norm of the two-dimensional (axis-parallel) discrepancy that can be obtained by K.Roth's orthogonal function method among a large class of test…
In this paper, we derive the continuity of solutions to the $L_{p}$ torsional Minkowski problem for $p>1$. It is shown that the weak convergence of the $L_{p}$ torsional measure implies the convergence of the sequence of the corresponding…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…
This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these…
We consider the differential entropy of probability measures absolutely continuous with respect to a given $\sigma$-finite reference measure on an arbitrary measurable space. We state the asymptotic equipartition property in this general…
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…