We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this paper, we handle the case of transient walks.
"One-dimensional long-range diffusion limited aggregation II: The transient case." Ann. Appl. Probab. 27 (3) 1886 - 1922, June 2017. https://doi.org/10.1214/16-AAP1248