Branched growth with eta approximately 4 walkers

Diffusion-limited aggregation has a natural generalization to the "eta models," in which eta random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial dimensionality d=2, there is an upper critical eta(c)=4 above which the fractal dimensionality of the clusters is D=1. I compute the first-order correction to D for eta<4, obtaining D=1 + 1/2 (4-eta). The methods used can also determine multifractal dimensions to first order in 4-eta.