Figure 6. The BBP Phase Change.

We ran a series of simulations, varying the sample size m and number of markers n but keeping the product at mn = 2²⁰. Thus the predicted phase change threshold is F_ST = 2⁻¹⁰. We vary F_S and plot the log p-value of the Tracy–Widom statistic. (We clipped −log₁₀ p at 20.) Note that below the threshold there is no statistical significance, while above threshold, we tend to get enormous significance.