Dispersion in the radii of gyration of diffusion-limited aggregates

Using a Gaussian stochastic model for configurational size fluctuations, we show that diffusion-limited aggregates asymptotically attain monodispersity (variance→0) in their radii of gyration (${\mathit{R}}_{\mathit{g}}$) in three dimensions and above. The decay of the variance in ${\mathit{R}}_{\mathit{g}}$ as function of the cluster mass is found to be the fastest in Euclidean dimension ${\mathit{d}}_{\mathit{c}}$=2+ √7 . However, in two dimensions, the variance is found to diverge with the mass. These results are a consequence of relating ${\mathit{R}}_{\mathit{g}}$ fluctuations to the width of the active zone of growth.