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Keywords = Sierpinski gasket graph

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13 pages, 4774 KiB  
Article
On the Fluctuations of Internal DLA on the Sierpinski Gasket Graph
by Nico Heizmann
Math. Comput. Appl. 2023, 28(3), 73; https://doi.org/10.3390/mca28030073 - 7 Jun 2023
Viewed by 1374
Abstract
Internal diffusion limited aggregation (IDLA) is a random aggregation model on a graph G, whose clusters are formed by random walks started in the origin (some fixed vertex) and stopped upon visiting a previously unvisited site. On the Sierpinski gasket graph, the [...] Read more.
Internal diffusion limited aggregation (IDLA) is a random aggregation model on a graph G, whose clusters are formed by random walks started in the origin (some fixed vertex) and stopped upon visiting a previously unvisited site. On the Sierpinski gasket graph, the asymptotic shape is known to be a ball in the graph metric. In this paper, we improve the sublinear bounds for the fluctuations known from its known asymptotic shape result by establishing bounds for the odometer function for a divisible sandpile model. Full article
(This article belongs to the Special Issue Geometry of Deterministic and Random Fractals)
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