SELF-SIMILARITY OF HARMONIC MEASURE ON DLA

The right-hand side of the f(alpha) curve of the harmonic measure on DLA is undefined. This does not necessarily imply that the harmonic measure and the DLA geometry are not self-similar. We show for off-lattice DLA that the right-hand tail satisfies a different rescaling rule. This Cauchy rescaling is compatible with self-similarity. The analysis is done on off-off-lattice DLA in which both the Brownian motion and the Laplace equation are off-lattice. The cluster sizes range between 32 and 50 000 atoms. The square lattice used to numerically estimate the Laplacian potential introduces a lower cutoff on the spatial resolution of this potential. We find a dependence of the right tail of the distribution of Holders alpha on this ultraviolet cutoff. Whereas the shape of the tail does depend on this ultraviolet lattice cutoff, the applicability of the collapse rules do not.