Talagrand, we also show that the exponential integrability of a γ-sub-Gaussian vector in an arbitrary separable Banach space. These two definitions of sub-Gaussian vectors and γ-sub-Gaussian vectors are not comparable, and neither of these definitions is a necessary condition for the exponential...
51 The second moment of symmetric square L-functions over Gaussian integers 48:43 Adversarial training through the lens of optimal transport 1:16:40 Central Limit Theorems in Analytic Number Theory 48:39 Kantorovich operators and their ergodic properties 1:02:06 L-Functions of Elliptic Curves ...
We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of $X$ exists. The estimator is...
The use of vector correlations to elucidate the photodissociation dynamics of CH<sub>3</sub>I, OCS, and glyoxal is discussed. The correlations occur between the vectors Ě, the electric vector of the photolysis light, μ, the transition dipole moment of the parent, v, the relative recoil...
We also investigate a random method to identify exactly any vector which has a relatively short support using linear subgaussian measurements as above. It turns out that our analysis, when applied to $\\{-1,1\\}$-valued vectors with i.i.d, symmetric entries, yields new information on the...
The second type of sparsity in a quadratic form comes from the setting where we randomly sample the elements of an anisotropic subgaussian vector Y = H X Y = H X where H \\in \\mathbb{R}^{mimes m} H \\in \\mathbb{R}^{mimes m} is an m imes m m imes m symmetric matrix; ...
MPSVectorDescriptor MobileCoreServices ModelIO MonoTouch.Dialog MonoTouch.Dialog.Utilities MonoTouch.NUnit MonoTouch.NUnit.UI MultipeerConnectivity NaturalLanguage Network NetworkExtension NewsstandKit NotificationCenter NUnit NUnit.Framework NUnit.Framework.Api NUnit.Framework.Builders NUnit.Framework.Constraints N...
This paper considers two sub-optimal transmission schemes for a family of parallel Gaussian vector broadcast channels. One of the schemes is based on the QR precoding of Ginis et al. (2000). In QR precoding, the maximum achievable throughput depends on the order in which users are encoded. ...
Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform Mathlib.MeasureTheory.Function.LpSpace.DomAct.Continuous Mathlib.Geometry.Euclidean.PerpBisector Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.Analysis.Convex.SpecificFunctions.Basic Mathlib.MeasureTheory.Group.Integral Mathlib.MeasureTheory....
Mathlib.NumberTheory.Zsqrtd.GaussianInt Mathlib.RingTheory.PolynomialAlgebra Mathlib.RingTheory.Localization.Defs Mathlib.Topology.ContinuousMap.CocompactMap Mathlib.RingTheory.Polynomial.HilbertPoly Mathlib.LinearAlgebra.Finsupp.LinearCombination Mathlib.Algebra.Category.CoalgebraCat.Basic Mathlib.Topology....