# THE PROBABILISTIC ESTIMATES ON THE LARGEST AND SMALLEST q-SINGULAR VALUES OF RANDOM MATRICES

In this paper, we study the q-singular values of random matrices with pre-Gaussian entries defined in terms of the q-quasinorm with 0 < q ≤ 1. In this paper, we mainly consider 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. Based on the results in probabilistic estimates on the largest q-singular value, we also give probabilistic estimates on the smallest q-singular value for pre-Gaussian random matrices.