Exact results on exponential screening in two-dimensional diffusion-limited aggregation

We present an exact expression for the rate of screening with time of an arbitrary point on a growing diffusion-limited aggregate, and use it to study the multifractal singularities α that correspond to strongly screened sites. We find that the time evolution of these singularities is controlled by the field at the lips (the outer corners) of the fjord. We show quantitatively that if the time evolution of the strongest singularity ${\mathrm{\alpha }}_{\max }$ is self-consistent with the growth process, the key issue is the process by which long fjords are generated. We analyze this process and find an asymptotic linear slope for the decreasing part of f(α). This form agrees with recent measurements [Barabasi and Vicsek, J. Phys. A 23, L729 (1990)] and excludes an infinite value of ${\mathrm{\alpha }}_{\max }$.