For fixed m, the rescaled volume of a random m-dimensional projection or section of an ell_p ball satisfies a CLT, an MDP, and an LDP with explicit limits as N grows.
A note on critical intersections of classical and Schatten $p$-balls
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
citation-role summary
background 1
citation-polarity summary
fields
math.PR 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Limit Theorems for the Volume of Random Projections and Sections of $\ell_p^N$-balls
For fixed m, the rescaled volume of a random m-dimensional projection or section of an ell_p ball satisfies a CLT, an MDP, and an LDP with explicit limits as N grows.