Polydispersity Effect and Universality of Finite-Size Scaling Function

We derive an equation for the existence probability E p for general percolation problem using an analytical argument based on exponential-decay behaviour of spatial correlation function. It is shown that the finite-size scaling function is well approximated by the error function. The present argument explain why it is universal. We use Monte Carlo simulation to calculate E p for polydisperse continuum percolation and find that mono- and polydisperse system have the same finite-size scaling function.