A note on critical intersections of classical and Schatten $p$-balls
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917903745417216 |
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| author | Sonnleitner, Mathias Thäle, Christoph |
| author_facet | Sonnleitner, Mathias Thäle, Christoph |
| contents | The purpose of this note is to study the asymptotic volume of intersections of unit balls associated with two norms in $\mathbb{R}^n$ as their dimension $n$ tends to infinity. A general framework is provided and then specialized to the following cases. For classical $\ell_p^n$-balls the focus lies on the case $p=\infty$, which has previously not been studied in the literature. As far as Schatten $p$-balls are considered, we concentrate on the cases $p=2$ and $p=\infty$. In both situations we uncover an unconventional limiting behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10635 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on critical intersections of classical and Schatten $p$-balls Sonnleitner, Mathias Thäle, Christoph Probability Functional Analysis 52A23 (Primary) 60F05 (Secondary) The purpose of this note is to study the asymptotic volume of intersections of unit balls associated with two norms in $\mathbb{R}^n$ as their dimension $n$ tends to infinity. A general framework is provided and then specialized to the following cases. For classical $\ell_p^n$-balls the focus lies on the case $p=\infty$, which has previously not been studied in the literature. As far as Schatten $p$-balls are considered, we concentrate on the cases $p=2$ and $p=\infty$. In both situations we uncover an unconventional limiting behavior. |
| title | A note on critical intersections of classical and Schatten $p$-balls |
| topic | Probability Functional Analysis 52A23 (Primary) 60F05 (Secondary) |
| url | https://arxiv.org/abs/2308.10635 |