  Three-dimensional Monte Carlo simulations provide a striking confirmation to
a recent theoretical prediction: the Brownian non-Gaussian diffusion of
critical self-avoiding walks. Although the mean square displacement of the
polymer center of mass grows linearly with time (Brownian behavior), the
initial probability density function is strongly non-Gaussian and crosses over
to Gaussianity only at large time. Full agreement between theory and
simulations is achieved without the employment of fitting parameters. We
discuss simulation techniques potentially capable of addressing the study of
anomalous diffusion under complex conditions like adsorption- or
Theta-transition.
