dimensions according to two criteria: $100\times4000$, $30\times5000$, and $50\times5000$ were chosen to investigate “representative" microarray situations. We chose the other to have a range of ratios and estimate how valuable the Tracy-Widom approximation would be in situations that could be considered classical, i.e one small dimension (less than 10) and one large (several hundreds to several thousands). For the sake of completeness, we redid the simulations presented in @imj and present in Table 2 the results obtained with $\tilde{\mu}_{np}$ and $\tilde{\sigma}_{np}$ as centering and scaling.

   TW Quantiles    TW    5$\times$5   10$\times$ 10   100$\times$ 100   5$\times$20   10$\times$ 40   100$\times$400
  -------------- ------ ------------ --------------- ----------------- ------------- --------------- ----------------
       -3.9       .01        0            0.002            0.008           0.001          0.004           0.008
      -3.18       .05      0.003          0.018            0.043           0.019          0.032           0.044
      -2.78       0.10     0.022          0.054            0.090           0.056          0.077           0.095
      -1.91       .30      0.217          0.257            0.295           0.262          0.279           0.294
      -1.27       .50      0.464          0.486            0.497           0.490          0.494           0.489
       -.59       .70      0.702          0.703            0.700           0.702          0.707           0.702
       0.45       .90      0.903          0.903            0.901           0.905          0.906           0.899
       0.98       .95      0.949          0.950            0.950           0.952          0.953           0.949
       2.02       .99      0.988          0.990            0.991           0.989          0.990           0.990

  : **Quality of the Tracy-Widom Approximation (Continued):** the columns have the same meaning as in Table 1. The ratio $p/n$ is smaller than 