Asymptotic theory of Schatten classes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914748154511360 |
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| author | Juhos, Michael Kabluchko, Zakhar Prochno, Joscha |
| author_facet | Juhos, Michael Kabluchko, Zakhar Prochno, Joscha |
| contents | The study of Schatten classes has a long tradition in geometric functional analysis and related fields. In this paper we study a variety of geometric and probabilistic aspects of finite-dimensional Schatten classes of not necessarily square matrices. Among the main results are the exact and asymptotic volume of the Schatten-$\infty$ unit ball, the boundedness of its isotropy constant, a Poincaré-Maxwell-Borel lemma for the uniform distribution on the Schatten-$\infty$ ball, and Sanov-type large deviations principles for the singular values of matrices sampled uniformly from the Schatten-$p$ unit ball for any $0 < p \leq \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic theory of Schatten classes Juhos, Michael Kabluchko, Zakhar Prochno, Joscha Functional Analysis Operator Algebras Probability 46B06, 52A23, 60F05, 60F10 (Primary) 52A22, 60D05 (Secondary) The study of Schatten classes has a long tradition in geometric functional analysis and related fields. In this paper we study a variety of geometric and probabilistic aspects of finite-dimensional Schatten classes of not necessarily square matrices. Among the main results are the exact and asymptotic volume of the Schatten-$\infty$ unit ball, the boundedness of its isotropy constant, a Poincaré-Maxwell-Borel lemma for the uniform distribution on the Schatten-$\infty$ ball, and Sanov-type large deviations principles for the singular values of matrices sampled uniformly from the Schatten-$p$ unit ball for any $0 < p \leq \infty$. |
| title | Asymptotic theory of Schatten classes |
| topic | Functional Analysis Operator Algebras Probability 46B06, 52A23, 60F05, 60F10 (Primary) 52A22, 60D05 (Secondary) |
| url | https://arxiv.org/abs/2404.07145 |