的矩阵偏差不等式ℓp-范数

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2023-06-15 DOI:10.1142/s2010326323500077

Yuan-Chung Sheu, Te-Chun Wang

引用次数: 0

摘要

受i.i.d.系综高斯矩阵的一般矩阵偏差不等式[R.Vershynin，《高维概率：数据科学应用导论》，剑桥统计与概率数学系列（剑桥大学出版社，2018），doi:10.1017/9781108231596 of Theorem 11.1.5]的启发，我们证明了这一性质适用于ℓ1≤p<；∞的p-范数和i.i.d.系综亚高斯矩阵，即具有i.i.d.均值为零、单位方差、亚高斯项的随机矩阵。由于我们的结果，我们从中建立了Johnson–Lindenstrauss引理ℓ2n空间到ℓpm空间。

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Matrix deviation inequality for ℓp-norm

Motivated by the general matrix deviation inequality for i.i.d. ensemble Gaussian matrix [R. Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, 2018), doi:10.1017/9781108231596 of Theorem 11.1.5], we show that this property holds for the $ℓ_{p}$ -norm with $1 \leq p < \infty$ and i.i.d. ensemble sub-Gaussian matrices, i.e. random matrices with i.i.d. mean-zero, unit variance, sub-Gaussian entries. As a consequence of our result, we establish the Johnson–Lindenstrauss lemma from $ℓ_{2}^{n}$ -space to $ℓ_{p}^{m}$ -space for all i.i.d. ensemble sub-Gaussian matrices.

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来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.