English

Internal DLA on Sierpinski gasket graphs

Probability 2020-08-26 v5 Statistical Mechanics Mathematical Physics Metric Geometry math.MP

Abstract

Internal diffusion-limited aggregation (IDLA) is a stochastic growth model on a graph GG which describes the formation of a random set of vertices growing from the origin (some fixed vertex) of GG. 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 GG 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.

Cite

@article{arxiv.1702.04017,
  title  = {Internal DLA on Sierpinski gasket graphs},
  author = {Joe P. Chen and Wilfried Huss and Ecaterina Sava-Huss and Alexander Teplyaev},
  journal= {arXiv preprint arXiv:1702.04017},
  year   = {2020}
}

Comments

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)

R2 v1 2026-06-22T18:17:30.122Z