Let and be the mixed-norm sequence space of real matrices endowed with the (quasi-)norm . We shall prove a Poincaré–Maxwell–Borel lemma for suitably scaled matrices chosen uniformly at random in the -unit balls , and obtain both central and non-central limit theorems for their -norms. We use those limit theorems to study the asymptotic volume distribution in the intersection of two mixed-norm sequence balls. Our approach is based on a new probabilistic representation of the uniform distribution on .
Electron. J. Probab.
29:
1-44
(2024).
DOI: 10.1214/24-EJP1158