Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
- 2 Curvature Calculations for Antitrees
- 3 Gromov–Lawson Tunnels with Estimates
- 4 Norm Convergence of the Resolvent for Wild Perturbations
- 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
- 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees
- 7 Internal DLA on Sierpinski Gasket Graphs
- 8 Universal Lower Bounds for Laplacians on Weighted Graphs
- 9 Critical Hardy Inequalities on Manifolds and Graphs
- 10 Neumann Domains on Graphs and Manifolds
- 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
- 12 Box Spaces: Geometry of Finite Quotients
- 13 Ramanujan Graphs and Digraphs
- 14 From Partial Differential Equations to Groups
- 15 Spectral Properties of Limit-Periodic Operators
- 16 Uniform Existence of the IDS on Lattices and Groups
7 - Internal DLA on Sierpinski Gasket Graphs
Published online by Cambridge University Press: 14 August 2020
Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
- 2 Curvature Calculations for Antitrees
- 3 Gromov–Lawson Tunnels with Estimates
- 4 Norm Convergence of the Resolvent for Wild Perturbations
- 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
- 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees
- 7 Internal DLA on Sierpinski Gasket Graphs
- 8 Universal Lower Bounds for Laplacians on Weighted Graphs
- 9 Critical Hardy Inequalities on Manifolds and Graphs
- 10 Neumann Domains on Graphs and Manifolds
- 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
- 12 Box Spaces: Geometry of Finite Quotients
- 13 Ramanujan Graphs and Digraphs
- 14 From Partial Differential Equations to Groups
- 15 Spectral Properties of Limit-Periodic Operators
- 16 Uniform Existence of the IDS on Lattices and Groups
Summary
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 graphmetric) with probability 1.
Keywords
- Type
- Chapter
- Information
- Analysis and Geometry on Graphs and Manifolds , pp. 126 - 155Publisher: Cambridge University PressPrint publication year: 2020
- 2
- Cited by