A conditional limit theorem for high-dimensional ℓᵖ-spheres

DOI10.1017/jpr.2018.71zbMath1405.60038arXiv1509.05442OpenAlexW2963156634MaRDI QIDQ4611270

Kavitar Ramanan, Steven Soojin Kim

Publication date: 17 January 2019

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05442

zbMATH Keywords

relative entropylarge deviationconditional limit theoremsurface measurecone measureGibbs conditioning principleWasserstein topology\(\ell^p\)-sphere

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Large deviations (60F10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Asymptotic theory of convex bodies (52A23)

Related Items (17)

Projections of the uniform distribution on the cube: a large deviation perspective ⋮ Weighted \(p\)-radial distributions on Euclidean and matrix \(p\)-balls with applications to large deviations ⋮ Sanov-type large deviations in Schatten classes ⋮ Sanov-type large deviations and conditional limit theorems for high-dimensional Orlicz balls ⋮ A Maxwell principle for generalized Orlicz balls ⋮ 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 ⋮ Large deviations, moderate deviations, and the KLS conjecture ⋮ Large deviations and localization of the microcanonical ensembles given by multiple constraints ⋮ Yet another note on the arithmetic-geometric mean inequality ⋮ High-dimensional limit theorems for random vectors in ℓpn-balls. II ⋮ Sharp asymptotics for \(q\)-norms of random vectors in high-dimensional \(\ell_p^n\)-balls ⋮ Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures ⋮ A new look at random projections of the cube and general product measures ⋮ An asymptotic thin shell condition and large deviations for random multidimensional projections ⋮ Thin-shell theory for rotationally invariant random simplices ⋮ Limit theorems for random points in a simplex

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