Related papers: Norms of sub-exponential random vectors
We study relatively uniformly continuous operator semigroups on ordered vector spaces and extend several recent results obtained by M. Kramar Fijavz, M. Kandic, M. Kaplin, and J. Gluck in the vector lattice setting to ordered vector spaces…
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…
Relatively recently it was proved that if $\Gamma$ is an arbitrary set, then any equivalent norm on $c_0(\Gamma)$ can be approximated uniformly on bounded sets by polyhedral norms and $C^\infty$ smooth norms, with arbitrary precision. We…
This work investigates the invariance of the non-necessarily finite uniform dimension and related concepts for subextensions in skew polynomial rings \mbox{$ \mathbb{S}=R[ \mathbf{\mathrm{X}}; \mathbf{\alpha} , \mathbf{\delta} ]$} of…
We give norm inequalities for some classical operators in amalgams spaces and in some subspace of Morrey space.
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $\mathbb R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all…
In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…
We investigate the norm of sums of independent vector-valued random variables in noncommutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class Sq^n in Sp(lq^m) with optimal order m = n^2.…
Asymmetric vector norms are generalizations of asymmetric norms, where the subadditivity inequality is understood in ordered vector space sense. This relation imposes strong conditions on the ordering itself. This note studies on these…
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…
We consider randomized Verblunsky parameters for orthogonal polynomials on the unit circle as they relate to the problem of Steklov, bounding the polynomials' uniform norm independent of $n$.
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for…
We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf…
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…
A start is made to redefining the topology of the spaces of normal states (density operators) by a new norm which is finite only for states of finite entropy. It is shown that a symmetrized version of the free energy difference between…
We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We…
In the framework of causal perturbation theory renormalization consists of the extension of distributions. We give the explicit form of a Lorentz invariant extension of a scalar distribution, depending on one difference of space time…
We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic…