Sanov-type large deviations in Schatten classes

DOI10.1214/19-AIHP989zbMath1445.60012arXiv1808.04862OpenAlexW3011008510MaRDI QIDQ2179617

Joscha Prochno, Zakhar Kabluchko, Christoph Thäle

Publication date: 13 May 2020

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.04862

zbMATH Keywords

eigenvaluessingular valuesrandom matrix theorySchatten classesCoulomb gasGaussian ensemblesasymptotic geometric analysislarge deviations principleshigh dimensional convexitymatrix unit balls

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Local theory of Banach spaces (46B07) Eigenvalues, singular values, and eigenvectors (15A18) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Large deviations (60F10) Random matrices (algebraic aspects) (15B52)

Related Items (16)

Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings ⋮ 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 and conditional limit theorems for high-dimensional Orlicz balls ⋮ Intersection of unit balls in classical matrix ensembles ⋮ Large deviations, moderate deviations, and the KLS conjecture ⋮ Yet another note on the arithmetic-geometric mean inequality ⋮ 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 ⋮ Gelfand numbers of embeddings of Schatten classes ⋮ Thin-shell theory for rotationally invariant random simplices ⋮ Exact asymptotic volume and volume ratio of Schatten unit balls ⋮ Asymptotics of the inertia moments and the variance conjecture in Schatten balls ⋮ Limit theorems for random points in a simplex ⋮ Large deviations for uniform projections of $p$-radial distributions on $\ell_p^n$-balls

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