14 indeed was seen numerically in [6], but the treatment was not systematic. This paper studies this issue in detail. In this situation, we see from the saddle point equations that the radius of the hole should be a function of q in the large N limit. However, for N finite there are corrections. The corrections from fluctuations about the saddle point are of order 1 /N $^{2}$, because N 2 is playing the role of ℏ in the saddle point approximation. There are also corrections due to granularity, for which there is currently no theoretical understanding as to how they systematically affect the correlations. The projection of the density of particles in the 12 plane gives us a disk with a hole in it. Let us assume that this picture from these simulations is correct geometrically. Therefore in the large N limit the saddle point density has no fluctuations (they are suppressed by 1 /N $^{2}$). Because of this we should be able to define a geometric radius of the inner radius of the distribution at N → ∞ . This should be measurable. Now, we need to find a good geometric description of the size of the hole that can be evaluated numerically for configurations that are not strictly at N = ∞ , but that have some fluctuations. This is, we want to find a radius function of the distribution that we can average over configurations We want the function r$_{0}$ (ˆ ρ, N ) to be as well behaved as possible. This is, we want the fluctuations of r$_{0}$ to be small. There is more than one such function. Let us consider various options. The arguments of planar diagrams suggest that good functions are traces over matrices. These are given in the thermodynamic limit by integrals over ρ (equivalently, integrals over ˆ ρ ). Consider for example the following numbers The quantities r$_{k}$ are natural. They weigh the points in the distribution by how far they are from the z 1 = 0 locus. For very large k , these are dominates by the smallest value r$_{0}$ that ˆ ρ can attain. These are also easy to compute numerically. This was the rationale for using them in our numerical codes and this choice was made before taking the data. We collected these for various k for many statistically independent configurations at different values of Q, N . We will explain the data later. r$_{0}$ ( N, q ) = 〈 r$_{0}$ (ˆ ρ, N ) 〉 (15) f$_{k}$ = r − 2 k k = ∫ ˆ ρ ( a ) 1 | ( a$_{1}$ ) 2 + ( a$_{2}$ ) $^{2}$|2 k (16)