Internal Diffusion Limited Aggregation on Discrete Groups Having Exponential Growth
By S'ebastien Blachere, S. Brofferio. 2005
59 citations recorded by the source corpus.
The internal diffusion limited aggregation (DLA) has been introduced by Diaconis and Fulton [Rend. Sem. Mat. Univ. Pol. Torino 49, 95–119 (1991)]. It is a growth model defined on an infinite set and associated to a Markov chain on this set. We focus here on sets which are finitely generated groups with exponential growth. We prove a shape theorem for the internal DLA on such groups associated to symmetric random walks. For that purpose, we introduce a new distance associated to the Green function, which happens to have some interesting properties. In the case of homogeneous trees, we also get the right order for the fluctuations of that model around its limiting shape.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2b9977f19053582c1a81a310848a64778d971678
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Harmonic measures versus quasiconformal measures for hyperbolic groups (2008, background): “This function dG is known to be a left-invariant metric on Γ (see [7, 8] for details).”
- Random walks on co-compact fuchsian groups (2013, unknown): “The Green metric associated with F 1 has been used by a number of authors, for instance in [7], [8] and [9].”
- Asymptotic entropy and Green speed for random walks on countable groups (2006, unknown): “When μ is symmetric and finitely supported, the two metrics dG(·, ·) and dw(·, ·) can be compared (see [4], Lemma 2.”