We derive estimates for the largest and smallest singular values of sparse rectangular random matrices, assuming . We consider a model with sparsity parameter such that for some , and assume that the moments of the matrix elements satisfy the condition . We assume also that the entries of matrices we consider are truncated at the level with .
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.
This article was first posted with one affiliation of A. Tikhomirov. The second affiliation “HSE University, Moscow, Russia” was added on 21 February 2023.
"On the largest and the smallest singular value of sparse rectangular random matrices." Electron. J. Probab. 28 1 - 18, 2023. https://doi.org/10.1214/23-EJP919