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- W4296567059 abstract "Let $p, q in (0, infty]$ and $ell_p^m(ell_q^n)$ be the mixed-norm sequence space of real matrices $x = (x_{i, j})_{i leq m, j leq n}$ endowed with the (quasi-)norm $Vert x Vert_{p, q} := bigVert big( Vert (x_{i, j})_{j leq n} Vert_q big)_{i leq m} Vert_p$. We shall prove a Poincar'e-Maxwell-Borel lemma for suitably scaled matrices chosen uniformly at random in the $ell_p^m(ell_q^n)$ unit balls $mathbb{B}_{p, q}^{m, n}$, and obtain both central and non-central limit theorems for their $ell_p(ell_q)$-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 $mathbb{B}_{p, q}^{m, n}$." @default.
- W4296567059 created "2022-09-21" @default.
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- W4296567059 date "2022-09-19" @default.
- W4296567059 modified "2023-09-30" @default.
- W4296567059 title "Limit theorems for mixed-norm sequence spaces with applications to volume distribution" @default.
- W4296567059 doi "https://doi.org/10.48550/arxiv.2209.08937" @default.
- W4296567059 hasPublicationYear "2022" @default.
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