Geometry of \(\ell_p^n\)-balls: classical results and recent developments

DOI10.1007/978-3-030-26391-1_9zbMath1456.46013arXiv1808.10435OpenAlexW2889524226MaRDI QIDQ2190638

Nicola Turchi, Christoph Thäle, Joscha Prochno

Publication date: 21 June 2020

Full work available at URL: https://arxiv.org/abs/1808.10435

zbMATH Keywords

law of large numberscentral limit theoremlarge deviationsasymptotic geometric analysis\(\ell_p^n\)-ballspolar integration formula

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Large deviations (60F10) Asymptotic theory of convex bodies (52A23) Asymptotic theory of Banach spaces (46B06)

Related Items (6)

Weighted \(p\)-radial distributions on Euclidean and matrix \(p\)-balls with applications to large deviations ⋮ Geometric sharp large deviations for random projections of \(\ell_p^n\) spheres and balls ⋮ 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 ⋮ A new look at random projections of the cube and general product measures ⋮ Large deviations for uniform projections of $p$-radial distributions on $\ell_p^n$-balls

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