Let $A$ be a $k\times n, k<n-1$ random matrix with entries drawn i.i.d. from a standard Gaussian, and $B$ a $k\times m$ random matrix with entries drawn i.i.d from a standard Gaussian, and independently of the entries of $A$.

Is there any upper bound known about the largest singular value of this matrix: $(BB^T)^{-1/2}A$?

  • 1
    $\begingroup$ The probability that the largest singular value exceeds $T$ should be something like $T^{-(n-k+1)}$. I do some closely related estimates in section 4.2.5 of my paper with Froyland and González-Tokman, arxiv.org/pdf/1310.2398 $\endgroup$ – Anthony Quas Sep 15 '15 at 4:38
  • 1
    $\begingroup$ The case $k=m$ is somewhat special, as it leads to the Jacobi ensemble (in particular edge asymptotics are known in great detail). See Forrester's book and also his recent article arxiv.org/pdf/1401.2572v2.pdf $\endgroup$ – ofer zeitouni Sep 17 '15 at 5:13

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.