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Asymptotic theory of Schatten classes
Michael Juhos, Zakhar Kabluchko, Joscha Prochno · 2024-04-11 · via math.PR updates on arXiv.org

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 $0 < p \leq \infty$.

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