On One-dimensional Multi-Particle Diffusion Limited Aggregation

TL;DR

This paper proves that in one-dimensional Multi-Particle Diffusion Limited Aggregation, the aggregate grows linearly when particle density exceeds 1, extending the result to all dimensions at this density.

Contribution

It establishes the linear growth of the model for densities above 1, answering a longstanding question and generalizing to higher dimensions.

Findings

Linear growth for density > 1 in 1D

Extension of linear growth result to all dimensions at density ≥ 1

Addresses a question posed by Kesten and Sidoravicius

Abstract

We prove that the one dimensional Multi-Particle Diffusion Limited Aggregation model has linear growth whenever the particle density exceeds 1 answering a question of Kesten and Sidoravicius. As a corollary we prove linear growth in all dimensions d when the particle density is at least 1.