Probabilistic Estimates of the Largest Strictly Convex Singular Values of Pregaussian Random Matrices

Abstract

In this study, the p-singular values of random matrices with Gaussian entries defined in terms of the l_p-p-norm for p>1, as is studied. Mainly, using analytical techniques, we show the probabilistic estimate, precisely, the decay, on the upper tail probability of the largest strictly convex singular values, when the number of rows of the matrices becomes very large and the lower tail probability of theirs as well. These results provide probabilistic description or picture on the behaviors of the largest p-singular values of random matrices in probability for p>1. Also, we show some numerical experiential results, which verify the theoretical results.