论文标题
$ p $ - 利基分布的均匀预测的大偏差$ \ ell_p^n $ -
Large deviations for uniform projections of $p$-radial distributions on $\ell_p^n$-balls
论文作者
论文摘要
我们考虑从$ \ Mathbb {r}^n $，$ k \ le n $的正常$ k $ frames的均匀随机变量的产物，以及$ n $ dimensional $ \ ell_p^n $ ball $ \ ell_pball $ \ mathbb {b} b}的$ n $ -dimensional $ \ ell_p^n $ with $ $ p \在[1，\ infty）$中。该产品的分布几何对应于$ \ Mathbb {b}^n_p $上$ p $ - 义务分布的投影，以在随机的$ k $ -dimeNsional子空间上。我们在$ \ mathbb {r}^k $上的概率度量空间中得出了大偏差原理（LDP），以进行此类预测的序列。
We consider products of uniform random variables from the Stiefel manifold of orthonormal $k$-frames in $\mathbb{R}^n$, $k \le n$, and random vectors from the $n$-dimensional $\ell_p^n$-ball $\mathbb{B}_p^n$ with certain $p$-radial distributions, $p\in[1,\infty)$. The distribution of this product geometrically corresponds to the projection of the $p$-radial distribution on $\mathbb{B}^n_p$ onto a random $k$-dimensional subspace. We derive large deviation principles (LDPs) on the space of probability measures on $\mathbb{R}^k$ for sequences of such projections.
