title: Scaling exponent of the maximum growth probability in diffusion-limited aggregation.
abstract: An early (and influential) scaling relation in the multifractal theory of diffusion limited aggregation (DLA) is the Turkevich-Scher conjecture that relates the exponent alpha(min) that characterizes the "hottest" region of the harmonic measure and the fractal dimension D of the cluster, i.e., D=1+alpha(min). Due to lack of accurate direct measurements of both D and alpha(min), this conjecture could never be put to a serious test. Using the method of iterated conformal maps, D was recently determined as D=1.713+/-0.003. In this paper, we determine alpha(min) accurately with the result alpha(min)=0.665+/-0.004. We thus conclude that the Turkevich-Scher conjecture is incorrect for DLA.
authors.affiliation: The Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark.
authors.forename: Mogens H
authors.initials: MH
authors.lastname: Jensen
authors.forename: Joachim
authors.initials: J
authors.lastname: Mathiesen
authors.forename: Itamar
authors.initials: I
authors.lastname: Procaccia