reduction procedures to gene grouping. Having a good understanding of the behavior of the singular values of gaussian “white noise" matrices could provide valuable insights for these applications. Recent work of @bl03 about the properties of naive Bayes and Fisher’s linear discriminant function when $p\gg n$ illustrates the impetus these dimensionality assumptions are also gaining in theoretical studies. Our work is part of the larger effort to investigate the properties of high dimensional data structures. Here it is done in a simple, “null" situation.

We now present a few numerical experiments we realized to assess how big (or small) $n$ or $p$ should be for Theorems \[ThJ\] and \[ThJextended\] to be practically useful.

Numerical experiments
---------------------

@imj showed empirically that in that situation the Tracy-Widom approximation was reasonably satisfying, even for small matrices. Similarly, to try to assess its accuracy in our setup, we ran the following experiments in `Matlab`: we picked $n$ and $p$ and generated $10,000$ $n\times p$ matrices $X$ with entries iid ${\cal
N}(0,1)$. Then we used standard routines (`normest` in `Matlab`) to compute their spectral norms and squared them to obtain a dataset of $l_1$-s.

Following [@imj2], we adjust centering and scaling to $$\begin{aligned}
\tilde{\mu}_{np}&=\sqrt{n-1/2}+\sqrt{p-1/2}\; ,\\
