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

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Abstract
We derive estimates for the largest and smallest singular values of sparse rectangular N×n random matrices, assuming limN,n→∞n N=y∈(0,1). We consider a model with sparsity parameter pN such that NpN∼logαN for some α>1, and assume that the moments of the matrix elements satisfy the condition E|Xjk|4+δ≤C<∞. We assume also that the entries of matrices we consider are truncated at the level (NpN)1 2−ϰ with ϰ:=δ 2(4+δ).

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