9 II. WAVE FUNCTIONS AND GEOMETRIC OBSERVABLES behaved 1 /N expansion at fixed k . We also review the argument that leads to a singular distribution of eigenvalues in the saddle point approximations. In section III we describe our numerical results for the wave functions. We describe data sets in various types of analyses. First we describe individual data sets for fixed Q, N . This lets us see the topology of the configuration from the plots and we also see that the support of the distribution of eigenvalues if of codimension one at large N , with fluctuations. We can also compare the different characterizations of the radius of the hole to see how big the fluctuations are on the various measurements and why some statistical characterizations of this feature are pathological (they are dominated by fluctuations). For the measurements that are well behaved we find that they converge at different rates, that one can mathematically prove some inequalities between them and that one such type of measurement converges faster and is optimal given our choices. Given this information, we then study the problem of varying N at fixed q = Q/N , to see how the large N limit is approached. Our numerical results show that the convergence to large N is slower than would be expected based on large N counting arguments. Finally, we also study the radius of the hole by varying q at fixed large N ( N = 10000) and obtain a scaling exponent of the radius as a function of q for small q . These results are different than those that were found previously in [6], that were obtained for much smaller values of N . We then conclude. The matrix model of commuting hermitian matrices X a [5] leads (by diagonalization of the matrices) to a model of N particles in six dimensions whose quantum Hamiltonian is given by H = ∑ i − 1 2 1 µ 2 ⃗ ∇ $_{i}$µ $^{2}$∇ i + 1 2 | ⃗ x$_{i}$ | 2 (2) where ⃗ x$_{i}$ are the positions of the particles in R 6 and µ 2 = ∏ i<j | ⃗ x$_{i}$ − ⃗ x$_{j}$ | 2 is a generalized Vandermonde determinant. The x a i are the i -th eigenvalue of the matrix X $^{a}$. The six x variables per eigenvalue can be written in complex notation in terms of three complex numbers √$_{2}$$_{z}$ a = x 2 a − 1 + ix 2 $^{a}$, which can be arranges as a vector ⃗ z and their complex conjugates ⃗ ¯ z per each eigenvalue.