THE PROBABILITY-DISTRIBUTION OF THE PERCOLATION-THRESHOLD IN A LARGE SYSTEM

We show that the distribution of the percolation threshold in a large finite system does not converge to a Gaussian when the size of the sys tem goes to infinity, provided that the two widely accepted definition s of correlation length are equivalent. The shape of the distribution is thus directly related to the presence or absence of logarithmic cor rections in the power law for the correlation length. The result is ob tained by estimating the rate of decay of tail of the limiting distrib ution in terms of the correlation length exponent upsilon. All results are rigorously proven in the 2D case. Generalizations for three dimen sions are also discussed.