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Title: Boundary conditions in Abelian sandpiles
Author: Gamlin, Samuel
ISNI:       0000 0004 5923 5293
Awarding Body: University of Bath
Current Institution: University of Bath
Date of Award: 2016
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The focus of this thesis is to investigate the impact of the boundary conditions on configurations in the Abelian sandpile model. We have two main results to present in this thesis. Firstly we give a family of continuous, measure preserving, almost one-to-one mappings from the wired spanning forest to recurrent sandpiles. In the special case of $Z^d$, $d \geq 2$, we show how these bijections yield a power law upper bound on the rate of convergence to the sandpile measure along any exhaustion of $Z^d$. Secondly we consider the Abelian sandpile on ladder graphs. For the ladder sandpile measure, $\nu$, a recurrent configuration on the boundary, I, and a cylinder event, E, we provide an upper bound for $\nu(E|I) − \nu(E)$.
Supervisor: Jarai, Antal Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Abelian sandpile ; spanning forest ; wilson's algorithm ; Random walk