2023/08/07 by Nico Heizmann, Robin Kaiser, Heizmann, Nico +3
Computer Science · Physics and Astronomy · #05C81 #31E05 #60J10 #60J45 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Theoretical and Computational Physics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2308.03445
openalex publication_date 2023/08/07 · openalex created_date 2023/08/09 · openalex updated_date 2026/07/28
For the Abelian sandpile model on Sierpinski graphs, we investigate several statistics such as average height, height probabilities and looping constant. In particular, we calculate the expected average height of a recurrent sandpile on the finite iterations of the Sierpinski gasket and we also give an algorithmic approach for calculating the height probabilities of recurrent sandpiles under stationarity by using the connection between recurrent configurations of the Abelian sandpile Markov chain and uniform spanning trees. We also calculate the expected fraction of vertices of height i for i∈\0,1,2,3\ of sandpiles under stationarity and relate the bulk average height to the looping constant on the Sierpinski gasket.