Hausdorff dimension and fluctuations for the largest cluster at the two-dimensional percolation threshold

Monte Carlo simulation shows the average mass of the largest cluster to increase asL ^1.9 at the percolation threshold inL × L square lattices,L290. This fractal dimension agrees with the finite-size scaling prediction/v for this exponent, in contrast to results of Halley and Thang Mai. The mean-square fluctuations in the mass of the largest cluster diverge with the same exponent/v1.8 as the susceptibility.