One-dimensional long-range Diffusion Limited Aggregation II: the transient case

TL;DR

This paper investigates the growth behavior of one-dimensional long-range diffusion-limited aggregation for transient random walks, providing bounds based on the moments of the step distribution.

Contribution

It offers new bounds on aggregate growth rates for transient walks with long jumps, extending understanding of DLA in one dimension.

Findings

Established upper and lower bounds on growth rates

Analyzed the effect of moments of step distribution

Focused on the transient case of walks

Abstract

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.