论文标题
限制具有应用程序的混合声 - 序列序列空间的定理到体积分布
Limit theorems for mixed-norm sequence spaces with applications to volume distribution
论文作者
论文摘要
令$ p，q \ in（0，\ infty] $和$ \ ell_p^m（\ ell_q^n）$是真实矩阵的混合序列空间$ x =（x_ {i，j}）_ {i \ leq m，j \ leq n} $ and（quas-qasi-quasi-） \ big \ vert \ big（\ vert（x_ {i，j}）_ {j \ leq n} \ vert_q \ big）_ {i \ leq m} \ vert_p $。 $ \ ell_p^m（\ ell_q^n）$单位球$ \ mathbb {b} _ {p，q}^{m，n} $，并获得中央和非中央限制定理的$ \ ell_p（\ ell_p（\ ell_q）$ - 我们使用这些限制序列方法基于$ \ mathbb {b} _ {p，q}^{m，n} $上均匀分布的新概率表示。
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 $\Vert x \Vert_{p, q} := \big\Vert \big( \Vert (x_{i, j})_{j \leq n} \Vert_q \big)_{i \leq m} \Vert_p$. We shall prove a Poincaré-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 $\mathbb{B}_{p, q}^{m, n}$.
