Diffusion-limited aggregation on the hyperbolic plane

TL;DR

This paper studies a diffusion-limited aggregation model on the hyperbolic plane, demonstrating that the resulting aggregate almost surely maintains a positive density at infinite time, revealing unique geometric growth properties.

Contribution

It introduces and analyzes a diffusion-limited aggregation model on the hyperbolic plane, establishing positive density of the aggregate at infinity, a novel extension beyond Euclidean spaces.

Findings

The aggregate on the hyperbolic plane has positive density at infinity.

The model extends DLA analysis to non-Euclidean geometry.

Almost sure convergence to a dense structure at infinity.

Abstract

We consider an analogous version of the diffusion-limited aggregation model defined on the hyperbolic plane. We prove that almost surely the aggregate viewed at time infinity will have a positive density.