THE SUPERIORITY OF THE MINIMAL SPANNING TREE IN PERCOLATION ANALYSES OF COSMOLOGICAL DATA SETS

In this work we demonstrate the ability of the minimal spanning tree ( MST) to duplicate the information contained within a percolation analy sis for a point data set. We show how to construct the percolation pro perties from the MST, finding roughly an order of magnitude improvemen t in the computer time required. We apply these statistics to particle -mesh simulations of large-scale structure formation. We consider pure ly scale-free Gaussian initial conditions [P(k) proportional to k(n), with n = -2, -1, 0 and +1] in a critical-density universe. We find, in general, that the mass of the percolating cluster is a much better qu antity by which to judge the onset of percolation than the length of t he percolating cluster.