Asymmetry in the percolation thresholds of fully penetrable disks with two different radii

We perform simulations of continuum gradient percolation to measure the percolation threshold of systems of fully penetrable disks of two different radii. As a function of volumetric proportion v, the percolation threshold phi(c)(v,lambda) is approximately symmetric about v=0.5 for a fixed ratio lambda of the radii. However, the difference from symmetry is strongly statistically significant. We also improve, by an order of magnitude, the measurement of the percolation threshold for disks of equal radius: phi(*)(c)=0.676 347 5(6).