  Finite-size scaling arguments naturally lead us to introduce a
coordinate-dependent diffusion coefficient in a Fokker-Planck description of
the late stage dynamics of unbiased polymer translocation through a membrane
pore. The solution for the probability density function of the chemical
coordinate matches the initial-stage subdiffusive regime and takes into account
the equilibrium entropic drive. Precise scaling relations connect the
subdiffusion exponent to the divergence with the polymer length of the
translocation time, and also to the singularity of the probability density
function at the absorbing boundaries. Quantitative comparisons with numerical
simulation data in $d=2$ strongly support the validity of the model and of the
predicted scalings.
