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

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). consider a model with sparsity parameter pN such that NpN∼logαN some α>1, assume moments matrix elements satisfy condition E|Xjk|4+δ≤C<∞. also entries matrices we are truncated at level (NpN)1 2−ϰ ϰ:=δ 2(4+δ).