Directed Diffusion-Limited Aggregation
S\'ebastien Martineau (UMPA-ENSL)
TL;DR
This paper introduces a directed variant of the Diffusion-Limited Aggregation model, providing new definitions, bounds on information propagation, and insights into the geometry of the infinite cluster, aiming to establish a shape theorem.
Contribution
It presents a novel directed version of the DLA model with multiple equivalent definitions and analytical results on its geometric and dynamical properties.
Findings
Bounds on the speed of information propagation
Characterization of the infinite cluster geometry
Framework towards a shape theorem
Abstract
In this paper, we define a directed version of the Diffusion-Limited-Aggregation model. We present several equivalent definitions in finite volume and a definition in infinite volume. We obtain bounds on the speed of propagation of information in infinite volume and explore the geometry of the infinite cluster. We also explain how these results fit in a strategy for proving a shape theorem for this model.
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