19 from wave functions to geometries is not really understood, so how the details of the wave function appear in the data are still obscured. Given enough data, one should be able –at lest in principle– to reconstruct the ‘theory’ from the output of the black box. What we have chosen to do is to use simple geometric observables that describe integrals over a geometry. If we had a more precise understanding of the data, this could be exploited to get a picture of local geometric information. The next step in our procedure is to examine the data of the moments of the inverse radius of the distribution and to check how big are the fluctuations, relative to the size of the moments for the same setup N = 10000 and Q = 100. This is the choice that we made before looking at the data. In particular, we are at first more interested in seeing how large are the fluctuations of these observables. This will give us a rough idea of how far from the large N limit we really are. In a certain sense, this is one of the most important pieces of information we can gather. If we expect some precision on the local geometry, we want basic geometric quantities to have low variance. If the variance is high, individual pictures of the data will be very fuzzy relative to the large N limit. The results of this analysis appear in the figure 2. The figure shows that the variance of the observables depends on the quantum numbers of the observables. A look of the data suggests a power law behavior. We can test this in a log plot, shown in figure 3. FIG. 2: On the left figure, the mean value of the moments at N = 10000, Q = 100, for k = 1 , . . . , 14. On the right, the statistical variance δf$_{k}$/f$_{k}$ . As can be seen, the variance in the values increase as we take k larger, and are already of order 10% for k = 14, which is a moderate value of k . This indicates that fluctuations start becoming important for relatively low values of k , even in the case where Q is large. For smaller Q the inner radius is smaller, and fluctuations of one outlying particle near the inner edge are even more important in f$_{k}$ . GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> 2 4 6 8 10 12 14 100 10 4 10 6 10 8 GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> 2 4 6 8 10 12 14 0.02 0.04 0.06 0.08 0.10