the Tracy-Widom Approximation for some large matrices:** the leftmost columns displays certain quantiles of the Tracy-Widom distribution. The second column gives the corresponding value of its cdf. Other columns give the value of the empirical distribution functions obtained from simulations at these quantiles. $\tilde{\mu}_{np}$ and $\tilde{\sigma}_{np}$ are the centering and scaling sequences.

\

   TW Quantiles   TW    50$\times$5000   50$\times$20000   50$\times$50000   5$\times$200   5$\times$2000   5$\times$20000
  -------------- ----- ---------------- ----------------- ----------------- -------------- --------------- ----------------
       -3.9       .01       0.010             0.017             0.021           0.008           0.014           0.018
      -3.18       .05       0.053             0.067             0.079           0.047           0.057           0.069
      -2.78       .10       0.104             0.125             0.139           0.094           0.110           0.120
      -1.91       .30       0.309             0.331             0.345           0.293           0.314           0.320
      -1.27       .50       0.502             0.522             0.538           0.500           0.506           0.519
      -0.59       .70       0.705             0.718             0.727           0.714           0.712           0.710
       0.45       .90       0.899             0.905             0.911           0.911           0.906           0.907
       0.98       .95       0.949             0.955             0.957           0.959           0.951           0.954
       2.02       .99       0.991             0.992             0.992           0.994           0.992           0.992

  : **Quality of the Tracy-Widom Approximation for some large matrices:** the leftmost columns displays certain quantiles of the Tracy-Widom distribution. The second column gives the corresponding value of its cdf. Other columns give the value of the empirical distribution functions obtained from simulations at these quantiles. $\tilde{\mu}_{np}$ and $\tilde{\sigma}_{np}$ are the centering and scaling sequences.

We picked the 