Boundary condition dependence of cluster size ratios in random percolation

We study the ratio of the number of sites in the largest and second largest clusters in random percolation. Using the scaling hypothesis that the rati o [M-1]/[M-2] of the mean cluster sizes M-1 and M-2 scales as f((p - p(c))L -1/nu), we employ finite-size scaling analysis to find that [M-1]/[M-2] is nonuniversal with respect to the boundary conditions imposed. The mean [M-1 /M-2] of the ratios behaves similarly although with a distinct critical val ue reflecting the relevance of mass fluctuations at the percolation thresho ld. These sere exponent ratios also allow for reliable estimates of the cri tical parameters at percolation from relatively small lattices.