On the largest and the smallest singular value of sparse rectangular random matrices

被引:1
作者
Gotze, F. [1 ]
Tikhomirov, A. [2 ,3 ]
机构
[1] Bielefeld Univ, Fac Math, Bielefeld, Germany
[2] RAS, Inst Phys & Math, Komi Sci Ctr, Ural Branch, Syktyvkar, Russia
[3] HSE Univ, Moscow, Russia
来源
ELECTRONIC JOURNAL OF PROBABILITY | 2023年 / 28卷
关键词
random matrices; sample covariance matrices; Marchenko-Pastur law; CIRCULAR LAW;
D O I
10.1214/23-EJP919
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We derive estimates for the largest and smallest singular values of sparse rectangular N x n random matrices, assuming lim(N,n ->infinity) n/N = y is an element of (0, 1). We consider a model with sparsity parameter p(N) such that N-pN similar to log(alpha) N for some alpha > 1, and assume that the moments of the matrix elements satisfy the condition E|X-jk|(4+delta) <= C < infinity. We assume also that the entries of matrices we consider are truncated at the level (NpN)(1/2-(sic)) with {(sic):= delta/2(4+delta).
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页数:18
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