Journal of Mathematics and Statistics

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

Yang Liu

DOI : 10.3844/jmssp.2015.7.15

Journal of Mathematics and Statistics

Volume 11, Issue 1

Pages 7-15

Abstract

In this study, the p-singular values of random matrices with Gaussian entries defined in terms of the lp-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.

Copyright

© 2015 Yang Liu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.