The Probabilistic Estimates on the Largest and Smallest q-Singular Values of Pre-Gaussian Random Matrices

We study the q-singular values of random matrices with pre-Gaussian entries dened in terms of the ‘q-quasinorm with 0 < q 1. Mainly we study the decay of the lower and upper tail probabilities of the largest q-singular value s (q) 1 , when the number of rows of the matrices becomes very large. Furthermore, we also give probabilistic estimates for the smallest q-singular value of pre-Gaussian random matrices.