Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings

Prochno, Joscha; Strzelecki, Michał

doi:10.1016/j.jat.2022.105736

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…The function p+ǫ,t satisfies the conditions of the Laplace principle (Proposition 2.11) by the same arguments as in the previous case. Thus, we can again apply the adapted Laplace principle from (6) to the limit in Λ +ǫ (t) in (33) Again, we consider the limit of Λ +ǫ as ǫ tends to zero, giving the lower bound for Λ(t):…”

Section: Singular Value Distribution For Non-self-adjoint Random Matr...mentioning

confidence: 99%

“…Barthe and Cordero-Erausquin [6] derived variance estimates, Radke and Vritsiou [36] proved the thin shell conjecture and Vritsiou [40] proved the variance conjecture for the operator norm in S n p . Hinrichs, Prochno and Vybiral [19,20] derived optimal bounds for the entropy numbers and sharp estimates for the Gelfand numbers of natural embeddings of S n p and Prochno and Strzelecki [33] also considered the approximation numbers of such embeddings and studied their relationship to the Gelfand and Kolmogorov numbers. Kabluchko, Prochno and Thäle [21,22] gave the exact asymptotic volumes and volume ratios of matrix p-balls and studied their intersection volumes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Weighted $p$-radial Distributions on Euclidean and Matrix $p$-balls with Applications to Large Deviations

Kaufmann¹,

Thaele²

2021

Preprint

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A probabilistic representation for a class of weighted p-radial distributions, based on mixtures of a weighted cone probability measure and a weighted uniform distribution on the Euclidean ℓ n p -ball, is derived. Large deviation principles for the empirical measure of the coordinates of random vectors on the ℓ n p -ball with distribution from this weighted measure class are discussed. The class of p-radial distributions is extended to p-balls in classical matrix spaces, both for self-adjoint and non-self-adjoint matrices. The eigenvalue distribution of a self-adjoint random matrix, chosen in the matrix p-ball according to such a distribution, is determined. Similarly, the singular value distribution is identified in the non-self-adjoint case. Again, large deviation principles for the empirical spectral measures for the eigenvalues and the singular values are presented as an application.

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Section: Singular Value Distribution For Non-self-adjoint Random Matr...mentioning

confidence: 99%