Internal DLA on Sierpinski gasket graphs

Abstract

Internal diffusion-limited aggregation (IDLA) is a stochastic growth model on a graph $G$ which describes the formation of a random set of vertices growing from the origin (some fixed vertex) of $G$. Particles start at the origin and perform simple random walks; each particle moves until it lands on a site which was not previously visited by other particles. This random set of occupied sites in $G$ is called the IDLA cluster. In this paper we consider IDLA on Sierpinski gasket graphs, and show that the IDLA cluster fills balls (in the graph metric) with probability 1.

24 pages, 2 figures. Final version, to appear as Chapter 7 of "Analysis and Geometry on Graphs and Manifolds," M. Keller, D. Lenz, and R.K. Wojciechowski, Cambridge University Press (2020)

References in corpus (1)

• Laplacian growth & sandpiles on the Sierpinski gasket: limit shape universality and exact solutions