Sharp asymptotics for \(q\)-norms of random vectors in high-dimensional \(\ell_p^n\)-balls

DOI10.15559/21-VMSTA182zbMath1476.60022arXiv2102.13513OpenAlexW3135149803MaRDI QIDQ2239804

Tom Kaufmann

Publication date: 5 November 2021

Published in: Modern Stochastics. Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.13513

zbMATH Keywords

precise large deviationsstrong large deviationslarge deviation principlessharp asymptoticssharp large deviationsasymptotic geometric analysis\(\ell_p^n\)-ballshigh-dimensional convexityvolume of convex bodies\(\ell_p^n\)-spheresintersection volume

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Large deviations (60F10) Probabilistic methods in Banach space theory (46B09) Asymptotic theory of convex bodies (52A23)

Related Items (2)

Large deviation principles induced by the Stiefel manifold, and random multidimensional projections ⋮ Geometric sharp large deviations for random projections of \(\ell_p^n\) spheres and balls

Cites Work

• Large deviations for random projections of \(\ell^{p}\) balls
• Approximate independence of distributions on spheres and their stability properties
• Power-law estimates for the central limit theorem for convex sets
• Large deviations techniques and applications.
• Sharp estimates of deviations of the sample mean in many dimensions
• Large deviations for high-dimensional random projections of \(\ell_p^n\)-balls
• A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
• Asymptotic approximations for multivariate integrals with an application to multinormal probabilities
• The maximum entropy principle and volumetric properties of Orlicz balls
• Sanov-type large deviations in Schatten classes
• Geometry of \(\ell_p^n\)-balls: classical results and recent developments
• Gaussian fluctuations for high-dimensional random projections of \(\ell_p^n\)-balls
• A central limit theorem for convex sets
• Curvature formulas for implicit curves and surfaces
• On Deviations of the Sample Mean
• The surface measure and cone measure on the sphere of ℓ_{𝑝}ⁿ
• Concentration phenomena in high dimensional geometry
• On the Volume of the Intersection of Two L n p Balls
• Fundamentals of Probability: A First Course
• The central limit problem for convex bodies
• A conditional limit theorem for high-dimensional ℓᵖ-spheres
• High-dimensional limit theorems for random vectors in ℓpn-balls
• High-Dimensional Probability
• Asymptotic Geometric Analysis, Part I
• Convex Analysis
• On the Probabilities of Large Deviations for Sums of Independent Random Variables
• Saddlepoint Approximations in Statistics
• Large deviations
• CLT and the volume of intersections of \(\ell_p^n\)-balls
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