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2023 On the largest and the smallest singular value of sparse rectangular random matrices
F. Götze, A. Tikhomirov
Author Affiliations +
Electron. J. Probab. 28: 1-18 (2023). DOI: 10.1214/23-EJP919


We derive estimates for the largest and smallest singular values of sparse rectangular N×n random matrices, assuming limN,nnN=y(0,1). We consider a model with sparsity parameter pN such that NpNlogαN for some α>1, and assume that the moments of the matrix elements satisfy the condition E|Xjk|4+δC<. We assume also that the entries of matrices we consider are truncated at the level (NpN)12ϰ with ϰ:=δ2(4+δ).

Funding Statement

F. Götze was supported by SFB 1283/2 2021—317210226. A.Tikhomirov was supported by the grant for research centers in the field of AI provided by the Analytical Center for the Government of the Russian Federation (ACRF) in accordance with the agreement on the provision of subsidies (identifier of the agreement 000000D730321P5Q0002) and the agreement with HSE University No. 70-2021-00139.

Version Information

This article was first posted with one affiliation of A. Tikhomirov. The second affiliation “HSE University, Moscow, Russia” was added on 21 February 2023.


Download Citation

F. Götze. A. Tikhomirov. "On the largest and the smallest singular value of sparse rectangular random matrices." Electron. J. Probab. 28 1 - 18, 2023.


Received: 8 November 2021; Accepted: 7 February 2023; Published: 2023
First available in Project Euclid: 13 February 2023

arXiv: 2207.03155
Digital Object Identifier: 10.1214/23-EJP919

Primary: 60B20

Keywords: Marchenko–Pastur law , random matrices , Sample covariance matrices

Vol.28 • 2023
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